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  • 1. Abascal, Isabel Sainz
    et al.
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Bipartite entanglement measure based on covariance2007In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 75, no 6Article in journal (Refereed)
    Abstract [en]

    We propose an entanglement measure for two quNits based on the covariances of a set of generators of the su(N) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this measure quantifies entanglement, we obtain an explicit expression which relates it to the concurrence hierarchy, specifically the I-concurrence and the three-concurrence. For mixed states we propose a separability criterion.

  • 2.
    Almlöf, Jonas
    et al.
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics (Closed 20120101), Quantum Electronics and Quantum Optics, QEO (moved to SCI 2011-07-01).
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics (Closed 20120101), Quantum Electronics and Quantum Optics, QEO (moved to SCI 2011-07-01).
    A short and efficient quantum-erasure code for polarization-coded photonic qubits2009In: CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, 2009, p. 5191786-Conference paper (Refereed)
  • 3.
    Almlöf, Jonas
    et al.
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
    Björk, Gunnar G. E.
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
    A short and efficient error correcting code for polarization coded photonic qubits in a dissipative channel2011In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 284, no 1, p. 550-554Article in journal (Refereed)
    Abstract [en]

    We propose a short and efficient non-degenerate quantum error correcting code that is adapted for qubits encoded on two orthogonal, single-photon states (e.g., horizontally and vertically polarized) subject to a dissipative channel. The proposed code draws its strength from the fact that it is adapted to the physical characteristics of the information-carrying basis states under the action of the channel. The code combines different energy manifolds and consists of only 3 spatio-temporal modes and on average 2 photons per code word.

  • 4.
    Almlöf, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Björk, Gunnar G. E.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Fidelity as a figure of merit in quantum error correction2013In: Quantum information & computation, ISSN 1533-7146, Vol. 13, no 1-2, p. 0009-0020Article in journal (Refereed)
    Abstract [en]

    We discuss the fidelity as a figure of merit in quantum error correction schemes. We show that when identifiable but uncorrectable errors occur as a result of the action of the channel, a common strategy that improves the fidelity actually decreases the transmitted mutual information. The conclusion is that while the fidelity is simple to calculate and therefore often used, it is perhaps not always a recommendable figure of merit for quantum error correction. The reason is that while it roughly speaking encourages optimisation of the "mean probability of success", it gives no incentive for a protocol to indicate exactly where the errors lurk. For small error probabilities, the latter information is more important for the integrity of the information than optimising the mean probability of success.

  • 5.
    Almlöf, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Björk, Gunnar G. E.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    On the efficiency of quantum error correction codes for the depolarising channelManuscript (preprint) (Other academic)
  • 6. Andersen, U. L.
    et al.
    Tipsmark, A.
    Laghaout, A.
    Dong, R.
    Jezek, M.
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics (Closed 20120101).
    Quantum information processing with discrete and continuous variables2011In: Optics InfoBase Conference Papers, 2011Conference paper (Refereed)
    Abstract [en]

    By means of a hybrid detector we suggest and implement two protocols. We theoretically propose a feasible loophole-free violation of Bell's inequality and we experimentally realize a Hadamard transform of coherent superposition states.

  • 7.
    Andersson, Mauritz
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Berglind, Eilert
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Orbital angular momentum modes do not increase the channel capacity in communication links2015In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 17, article id 043040Article in journal (Refereed)
    Abstract [en]

    The orbital momentum of optical or radio waves can be used as a degree of freedom to transmit information. However, mainly for technical reasons, this degree of freedom has not been widely used in communication channels. The question is if this degree of freedom opens up a new, hitherto unused 'communication window' supporting 'an infinite number of channels in a given, fixed bandwidth' in free space communication as has been claimed? We answer this question in the negative by showing that on the fundamental level, the mode density, and thus room for mode multiplexing, is the same for this degree of freedom as for sets of modes lacking angular momentum. In addition we show that modes with angular momentum are unsuitable for broadcasting applications due to excessive crosstalk or a poor signal-to-noise ratio.

  • 8. Asplund, R.
    et al.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Reconstructing the discrete Wigner function and some properties of the measurement bases2001In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 6401, no 1Article in journal (Refereed)
    Abstract [en]

    We derive a direct reconstruction algorithm for the discrete Wigner function through different types of measurements. For a system described in a Hilbert space of dimension N=N-1...N-p, where the numbers N-i are prime, the reconstruction is accomplished with (N-1+1)...(N-p+1) factorable (local) von Neumann measurements. For the special case where the dimension is a power of a prime, the reconstruction can be performed in a much more efficient way using N+1 complementary measurements. If the system is composed of a number of smaller subsystems, these measurements will then in general be nonseparable.

  • 9. Asplund, R.
    et al.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Bourennane, M.
    An expectation value expansion of Hermitian operators in a discrete Hilbert space2001In: Journal of Optics B-Quantum and Semiclassical Optics, ISSN 1464-4266, E-ISSN 1741-3575, Vol. 3, no 3, p. 163-170Article in journal (Refereed)
    Abstract [en]

    We discuss a real-valued expansion of any Hermitian operator defined in a Hilbert space of finite dimension N, where N is a prime number, or an integer power of a prime. The expansion has a direct interpretation in terms of the operator expectation values for a set of complementary bases. The expansion can be said to be the complement of the discrete Wigner function. We expect the expansion to be of use in quantum information applications since qubits typically are represented by a discrete, and finite-dimensional, physical system of dimension N = 2(p), where p is the number of qubits involved. As a particular example we use the expansion to prove that an intermediate measurement basis (a Breidbart basis) cannot be found if the Hilbert space dimension is three or four.

  • 10. Barnes, W. L.
    et al.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Gerard, J. M.
    Jonsson, P.
    Wasey, J. A. E.
    Worthing, P. T.
    Zwiller, V.
    Solid-state single photon sources: light collection strategies2002In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 18, no 2, p. 197-210Article in journal (Refereed)
    Abstract [en]

    We examine the problem of efficiently collecting the photons produced by solid-state single photon sources. The extent of the problem is first established with the aid of simple physical concepts. Several approaches to improving the collection efficiency are then examined and are broadly categorized into two types. First are those based on cavity quantum dynamics, in which the pathways by which the source may emit a photon are restricted, thus channeling emission into one desired mode. Second are those where we try to reshape the free space modes into a target mode in an optimal way, by means of refraction, without fundamentally altering the way in which the source emits. Respectively, we examine a variety of microcavities and solid immersion lenses. Whilst we find that the micropillar microcavities offer the highest collection efficiency (similar to70%), choosing this approach may not always be appropriate due to other constraints. Details of the different approaches, their merits and drawbacks are discussed in detail.

  • 11.
    Bayraktar, Ömer
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Swillo, Marcin
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Canalias, Carlota
    KTH, School of Engineering Sciences (SCI), Applied Physics, Laser Physics.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Quantum-polarization state tomography2016In: PHYSICAL REVIEW A, ISSN 2469-9926, Vol. 94, no 2, article id 020105Article in journal (Refereed)
    Abstract [en]

    We propose and demonstrate a method for quantum-state tomography of qudits encoded in the quantum polarization of N-photon states. This is achieved by distributing N photons nondeterministically into three paths and their subsequent projection, which for N = 1 is equivalent to measuring the Stokes (or Pauli) operators. The statistics of the recorded N-fold coincidences determines the unknown N-photon polarization state uniquely. The proposed, fixed setup manifestly rules out any systematic measurement errors due to moving components and allows for simple switching between tomography of different states, which makes it ideal for adaptive tomography schemes.

  • 12. Bengtsson, Ingemar
    et al.
    Björk, GunnarKTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.Bourennane, Mohamed
    International Conference on Quantum Information and Computation, Stockholm, 4-8 October, 2010: Book of Abstracts2010Conference proceedings (editor) (Other academic)
  • 13.
    Berglind, Eilert
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Humblet's Decomposition of the Electromagnetic Angular Moment in Metallic Waveguides2014In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 62, no 4, p. 779-788Article in journal (Refereed)
    Abstract [en]

    In a seminal paper, Humblet decomposed the angular momentum of a classical electromagnetic field as a sum of three terms: the orbital angular momentum (OAM), the spin, and the more unfamiliar surface angular momentum. In this paper, we present the result of such decomposition for various metallic waveguides. We investigate two hollow metal waveguides with circular and rectangular cross sections, respectively. The waveguides are excited with two TE eigenmodes driven in phase quadrature. As references, two better known modes are also analyzed: a plane, a circularly polarized wave (a TEM mode), and a TE-Bessel beam, both of infinite transverse extent and with no metallic boundaries. Our analysis shows that modes carrying OAM and spin can also propagate in the metallic waveguides, even when the cross section of the waveguide is distinctly non-circular. However, the mode density of orthogonal modes carrying OAM is at most equal to that of the waveguides' eigenmodes.

  • 14.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    20th Central European Workshop on Quantum Optics, Stockholm, June 16-20, 2013: Book of Abstracts2013Conference proceedings (editor) (Other academic)
  • 15.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Information gain when measuring an unknown qubit2018In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 1, article id 015403Article in journal (Refereed)
    Abstract [en]

    In quantum information the fundamental information-containing system is the qubit. A measurement of a single qubit can at most yield one classical bit. However, a dichotomous measurement of an unknown qubit will yield much less information about the qubit state. We use Bayesian inference to compute how much information one progressively gets by making sucessive, individual measurements on an ensemble of identically prepared qubits. Perhaps surprisingly, even if the measurements are arranged so that each measurement yields one classical bit, that is, the two possible measurement outcomes are a priori equiprobable, it takes almost a handful of measurements before one has gained one bit of information about the gradually concentrated qubit probability density. We also show that by following a strategy that reaps the maximum information per measurement, we are led to a mutually unbiased basis as our measurement bases. This is a pleasing, although not entirely surprising, result.

  • 16.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    de Guise, H.
    Klimov, A. B.
    de la Hoz, P.
    Sanchez-Soto, L. L.
    Classical distinguishability as an operational measure of polarization2014In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 90, no 1, p. 013830-Article in journal (Refereed)
    Abstract [en]

    We put forward an operational degree of polarization that can be extended in a natural way to fields whose wave fronts are not necessarily planar. This measure appears as a distance from a state to the set of all of its polarization-transformed counterparts. By using the Hilbert-Schmidt metric, the resulting degree is a sum of two terms: one is the purity of the state and the other can be interpreted as a classical distinguishability, which can be experimentally determined in an interferometric setup. For transverse fields, this reduces to the standard approach, whereas it allows one to get a straight expression for nonparaxial fields.

  • 17.
    Björk, Gunnar G.
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Kothe, Christian
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Bourennane, M.
    Inoue, S.
    Limits to the efficiency of quantum lithography2011In: Conf. Lasers Electro-Opt. Europe Eur. Quantum Electron. Conf., CLEO EUROPE/EQEC, 2011, p. 5943416-Conference paper (Refereed)
    Abstract [en]

    Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. The price to be paid is that the lithographic film must consist of a multi-photon absorbing material. If N photons are absorbed, the minimum feature resolution goes from roughly /2 to /2N. However, there has been a discussion in the literature as to what is the probability of N photons in a lithographic exposure field to hit the same detector pixel, thereby enabling the needed N-photon absorption. On one hand it has been claimed that If the optical system is aligned properly, the probability of the first photon arriving in a small absorptive volume of space time is proportional to [the field intensity]. However, the remaining N-1 photons are constrained to arrive at the same place at the same time [1]. On the other hand it has been argued that it is not true that the first arriving photon greatly constrains the arrival location of the following ones Very few photons will be absorbed in one point since they typically arrive far apart. [2]. The answer to this dispute dictate very much the practical feasibility of quantum lithography, because if the few photons in the entangled state are spread out over the exposed area, the probability will quickly become negligible that they arrive at the same spot (causing a N-photon detection event). This will render quantum lithography very inefficient, albeit still feasible in principle.

  • 18.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Grassl, Markus
    de la Hoz, Pablo
    Leuchs, Gerd
    Sanchez-Soto, Luis L.
    Stars of the quantum Universe: extremal constellations on the Poincare sphere2015In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 90, no 10, article id 108008Article in journal (Refereed)
    Abstract [en]

    The characterization of the polarization properties of a quantum state requires the knowledge of the joint probability distribution of the Stokes variables. This amounts to assessing all the moments of these variables, which are aptly encoded in a multipole expansion of the density matrix. The cumulative distribution of these multipoles encapsulates in a handy manner the polarization content of the state. We work out the extremal states for that distribution, finding that SU(2) coherent states are maximal to any order, so they are the most polarized allowed by quantum theory. The converse case of pure states minimizing that distribution, which can be seen as the most quantum ones, is investigated for a diverse range of number of photons. Exploiting the Majorana representation, the problem appears to be closely related to distributing a number of points uniformly over the surface of the Poincare sphere.

  • 19.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Inoue, S.
    Soderholm, J.
    Visibility is not a good measure of a well-defined relative phase2000In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 6202, no 2Article in journal (Refereed)
    Abstract [en]

    In a recent paper Marburger and Das [J. H. Marburger III and K. K. Das, Phys. Rev. A 59, 2213 (1999)] considered an interference visibility experiment involving two weakly interacting Bose-Einstein condensates. It was shown that condensate eigenstates of the Hermitian relative phase operator do not give interference fringes with unit visibility in a Young's double slit type of experiment. The authors concluded that ... these states are not especially well suited to describe weakly interacting multiply occupied coherent bosonic systems. In this work we suggest a criterion for states with a well-defined relative phase. Subsequently we show that the relative phase operator eigenstates satisfy this criterion. This suggests that the concept of interference visibility can, and should, be generalized, since it is widely believed that interference visibility is a measure of the relative phase properties. We therefore propose a broader, but still operational, definition of interference visibility, which we call generalized visibility, and prove that the relative phase operator eigenstates indeed can show unit generalized visibility. We also derive a simple, but general, criterion for states which can display a unit generalized visibility. Somewhat surprisingly, this criterion is weaker than the criterion for a well-defined relative phase. Finally, we discuss which two-mode states can display unit (ordinary) visibility.

  • 20.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Jonsson, P.
    Heydari, H.
    Soderholm, J.
    Hessmo, B.
    Hilbert space factorization and partial measurements2003In: Optics and Spectroscopy, ISSN 0030-400X, E-ISSN 1562-6911, Vol. 94, no 5, p. 695-699Article in journal (Refereed)
    Abstract [en]

    A quantum system whose state vector belongs to a finite-dimensional Hilbert space is considered. If this space has a dimension that is a composite number, one can factor the space into a tensor product of subspaces. An observable that acts only in one of these subspaces is called a partial measurement. Some of the properties and the interpretation of such partial measurements are discussed.

  • 21.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Jonsson, P.
    Sanchez-Soto, L. L.
    Single-particle nonlocality and entanglement with the vacuum2001In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 6404, no 4Article in journal (Refereed)
    Abstract [en]

    We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.

  • 22.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Klimov, A. B.
    Univ Guadalajara, Dept Fis, Guadalajara 44420, Jalisco, Mexico..
    de la Hoz, P.
    Univ Complutense Madrid, Dept Opt, Fac Fis, E-28040 Madrid, Spain..
    Grassl, M.
    Max Planck Inst Phys Lichts, D-91058 Erlangen, Germany.;Univ Erlangen Nurnberg, Inst Opt Informat & Photon, D-91058 Erlangen, Germany..
    Leuchs, G.
    Max Planck Inst Phys Lichts, D-91058 Erlangen, Germany.;Univ Erlangen Nurnberg, Inst Opt Informat & Photon, D-91058 Erlangen, Germany..
    Sanchez-Soto, L. L.
    Univ Complutense Madrid, Dept Opt, Fac Fis, E-28040 Madrid, Spain.;Max Planck Inst Phys Lichts, D-91058 Erlangen, Germany.;Univ Erlangen Nurnberg, Inst Opt Informat & Photon, D-91058 Erlangen, Germany..
    Extremal quantum states and their Majorana constellations2015In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 3, article id 031801Article in journal (Refereed)
    Abstract [en]

    The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those multipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states are maximal to any order whereas the converse case of minimal states (which can be seen as the most quantum ones) is investigated for a diverse range of the number of photons. Taking advantage of the Majorana representation, we recast the problem as that of distributing a number of points uniformly over the surface of the Poincare sphere.

  • 23.
    Björk, Gunnar
    et al.
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.
    Klimov, Andrei B.
    Sanchez-Soto, Luis L.
    The discrete Wigner function2008In: Progress in optics / [ed] Wolf, E, 2008, Vol. 51, p. 469-516Chapter in book (Refereed)
  • 24.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Laghaout, Amine
    Andersen, Ulrik L.
    Deterministic teleportation using single-photon entanglement as a resource2012In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 2, p. 022316-Article in journal (Refereed)
    Abstract [en]

    We outline a proof that teleportation with a single particle is, in principle, just as reliable as with two particles. We thereby hope to dispel the skepticism surrounding single-photon entanglement as a valid resource in quantum information. A deterministic Bell-state analyzer is proposed which uses only classical resources, namely, coherent states, a Kerr nonlinearity, and a two-level atom.

  • 25.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Man'ko, Margarita
    20th Central European Workshop on Quantum Optics Preface2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T160, p. 010301-Article in journal (Refereed)
  • 26.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Porta Mana, Piero Giovanni Luca
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    A size criterion for macroscopic superposition states2004In: Journal of Optics B-Quantum and Semiclassical Optics, ISSN 1464-4266, E-ISSN 1741-3575, Vol. 6, no 11, p. 429-436Article in journal (Refereed)
    Abstract [en]

    An operational measure to quantify the sizes of some 'macroscopic quantum superpositions', realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric applications than its superposed constituent states. This enhanced sensitivity, or 'interference utility', may then be used as a size criterion among superpositions.

  • 27.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Porta Mana, Piero Giovanni Luca
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Schrödinger-cat states: size classification based on evolution or dissipation2004In: Proceedings of SPIE - The International Society for Optical Engineering: Vol. 5468 / [ed] Heszler P; Abbott D; GeaBanacloche JR; Hemmer PR, 2004, p. 335-343Conference paper (Refereed)
    Abstract [en]

    The issue of estimating how "macroscopic" a superposition state is, can be addressed by analysing the rapidity of the state's evolution under a preferred observable, compared to that of the states forming the superposition. This fast evolution. which arises from the larger dispersion of the superposition state for the preferred operator, also represents a useful characteristic for interferometric applications. This approach can be compared to others in which a superposition's macroscopality is estimated in terms of the fragility to dissipation.

  • 28.
    Björk, Gunnar
    et al.
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Romero, Jose L.
    Klimov, Andrei B.
    Sanchez-Soto, Luis L.
    Mutually unbiased bases and discrete Wigner functions2007In: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 24, no 2, p. 371-378Article in journal (Refereed)
    Abstract [en]

    Mutually unbiased bases and discrete Wigner functions are closely but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime N=d(n), which describes a composite system of n qudits. Hence, entanglement naturally enters the picture. Although our results are general, we concentrate on the simplest nontrivial example of dimension N=8=2(3). It is shown that the number of fundamentally different Wigner functions is severely limited if one simultaneously imposes translational covariance and that the generating operators consist of rotations around two orthogonal axes, acting on the individual qubits only.

  • 29.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Sanchez-Soto, L. L.
    Soderholm, J.
    Entangled-state lithography: Tailoring any pattern with a single state2001In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 86, no 20, p. 4516-4519Article in journal (Refereed)
    Abstract [en]

    We demonstrate a systematic approach to Heisenberg-Limited lithographic image formation using four-mode reciprocal binomial states. By controlling the exposure pattern with a simple bank of birefringent plates, any pixel pattern on a (N + 1) X (N + 1) grid, occupying a square with the side half a wavelength long, can be generated from a 2N-photon state.

  • 30.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Sanchez-Soto, L. L.
    Soderholm, J.
    Subwavelength lithography over extended areas2001In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 6401, no 1Article in journal (Refereed)
    Abstract [en]

    We demonstrate a systematic approach to subwavelength resolution Lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of lambda/[2(N+1)] by using a particular 2M-photon, multimode entangled state, where N less than or equal toM, and banks of birefringent plates. By preparing such a statistically mixed state, one can form any pixel pattern on a 2(M-N)(N+1) x 2(M-N)(N+1) pixel grid occupying a square with side L = 2(M-N-1)lambda. Hence, there is a trade off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under nonideal conditions, albeit with somewhat poorer performance.

  • 31.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Shabbir, Saroosh
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Non-monotonic projection probabilities as a function of distinguishability2014In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, no 1, article id 013006Article in journal (Refereed)
    Abstract [en]

    Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference a non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more photons. We show that such a non-monotonic behavior of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.

  • 32.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Shabbir, Saroosh
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Non-monotonic projection probabilities as a function of distinguishability2014In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, p. 013006-Article in journal (Refereed)
    Abstract [en]

    Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference a non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more photons. We show that such a non-monotonic behavior of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.

  • 33.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Shabbir, Saroosh
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Reply to comment on ‘non-monotonic projection probabilities as a function of distinguishability’2014In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, no 11, article id 118004Article in journal (Refereed)
  • 34.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Shabbir, Saroosh
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Reply to comment on 'non-monotonic projection probabilities as a function of distinguishability'2014In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 16, p. 118004-Article in journal (Other academic)
    Abstract [en]

    We reiterate that a non-monotonic behavior of projection probabilities can occur for most states irrespective of the number of particles involved, based solely on the choice of the projectors chosen for measurement. We further clarify that, contrary to the claim in the comment, our analysis is not intended to demonstrate quantum to classical transition. However, our results show that a non-monotonic behavior is not a necessarily a signature of such a transition.

  • 35.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Soderholm, J.
    Trifonov, A.
    Tsegaye, T.
    A theory of the relative phase and number difference of two quantized harmonic oscillators2002In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T102, p. 133-146Article in journal (Refereed)
    Abstract [en]

    We present a comprehensive and self-consistent theory of relative-phase measurements and the associated Hermitian relative-phase operator of two harmonic oscillators. We find that since Nature does not favor any particular initial condition of the two oscillators, the relative-phase operator is not unique. We show that the relative-phase eigenstates; are maximally entangled. Therefore. most relative-phase operators lack a classical correspondence, even in the high-excitation limit. Furthermore, we find that the relative phase and the excitation number difference are noncommuting, noncanonical observables and we derive a commutation relation.

  • 36.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO. AlbaNova University Center, Sweden.
    Stensson, Katarina
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO. AlbaNova University Center, Sweden.
    Karlsson, Magnus
    Proposed Implementation of "Non-Physical" Four-Dimensional Polarization Rotations2016In: Journal of Lightwave Technology, ISSN 0733-8724, E-ISSN 1558-2213, Vol. 34, no 14, p. 3317-3322Article in journal (Refereed)
    Abstract [en]

    Recently one of us proposed a new formalism for modeling electromagnetic wave transformations for coherent communication using a real, four-vector description instead of the conventionally used Jones calculus or the Mueller matrices. The four-vector can then handle all superpositions of two orthogonal polarization basis and two orthogonal time bases (e.g., the in-phase and quadrature phase). In developing this formulation it was found that to provide a general but minimal framework for such rotations, it is natural to divide the six generators of four-dimensional (4d) rotations into two groups of three generators, the right-and the left-isoclinic matrices. Of the six transformations these generators define, it was furthermore found that four of them are readily implemented by linear optical components, while two of then were impossible to implement by such means. In this paper, we detail the reason these two "unphysical" rotations cannot be implemented with linear optics. We also suggest how they can be implemented, but at a cost in the signal-to-noise ratio, and give this minimum cost.

  • 37.
    Björk, Gunnar
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Söderholm, J.
    Kim, Y-S
    Ra, Y-S
    Lim, H-T
    Kothe, C.
    Kim, Y-H
    Sánchez-Soto, L. L.
    Klimov, A. B.
    Central-moment description of polarization for quantum states of light2012In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 5, p. 053835-Article in journal (Refereed)
    Abstract [en]

    We present a moment expansion for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincare sphere and provide a scheme for polarization tomography without resorting to full-state tomography. We apply these ideas to the experimental first-and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.

  • 38.
    Björk, Gunnar
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Söderholm, Jonas
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Sanchez-Soto, L. L.
    Two-photon imaging and quantum holography2004In: Journal of Optics B-Quantum and Semiclassical Optics, ISSN 1464-4266, E-ISSN 1741-3575, Vol. 6, no 6, p. S478-S482Article in journal (Refereed)
    Abstract [en]

    We discuss when the use of entangled photon pairs in an imaging system can be simulated with a classically correlated source. In particular, we consider two recently proposed schemes with 'bucket detection' of one of the photons. We argue that these schemes give identical results for entangled states as for appropriately prepared classically correlated states.

  • 39.
    Björk, Gunnar
    et al.
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
    Söderholm, Jonas
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
    Sanchez-Soto, Luis L.
    Klimov, Andrei B.
    Ghiu, Iulia
    Marian, Paulina
    Marian, Tudor A.
    Quantum degrees of polarization2010In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 283, no 22, p. 4440-4447Article in journal (Refereed)
    Abstract [en]

    We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.

  • 40.
    Blom, Hans
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Bark, Niklas
    Gösch, Michael
    Forsberg, Erik
    Heino, Toni
    Holm, Johan
    Björk, Gunnar
    Rigler, Rudolf
    Elliptical line focus in fluorescence spectroscopy: theory and applicationManuscript (preprint) (Other academic)
  • 41.
    Blom, Hans
    et al.
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Bark, Niklas
    Gösch, Michael
    Henriksson, Per
    Sigmundsson, Toni
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Rigler, Rudolf
    Analysis of amyloid β-peptides in fluid microchannelsManuscript (preprint) (Other academic)
  • 42.
    Blom, Hans
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
    Lorentzian spatial intensity distribution in one-photon fluorescence correlation spectroscopy2009In: Applied Optics, ISSN 1559-128X, E-ISSN 2155-3165, Vol. 48, no 31, p. 6050-6058Article in journal (Refereed)
    Abstract [en]

    The theory of autocorrelation-function evaluation in fluorescence correlation spectroscopy is applied to a Lorentzian intensity distribution. An analytical solution to the autocorrelation function for diffusion is deduced for this spatial distribution. Experimental investigation of the distribution is performed using an enlarged detector aperture in a standard confocal setup. The data from the experiment are fitted to the derived autocorrelation function, and a reasonable estimate of the spatial distribution is provided. Estimates are also compared to values computed by molecular detection efficiency simulation. The use of Lorentzian intensity distributions complements conditions where a Gaussian intensity distribution applies, expanding the applicability range of analytical correlation functions.

  • 43.
    Blom, Hans
    et al.
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Gösch, Michael
    Rigler, Rudolf
    Fluorescence correlation spectroscopy with Lorentzian intensity distributionManuscript (preprint) (Other academic)
  • 44. Bourennane, M.
    et al.
    Karlsson, Anders
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Quantum key distribution using multilevel encoding2001In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 6401, no 1Article in journal (Refereed)
    Abstract [en]

    In this article, protocols for quantum key distribution based on encoding in higher dimensional systems in N-dimensional Hilbert space are proposed. We extend the original Bennett-Brassard protocol using two complementary bases and two-dimensional states to M mutually complementary bases and N orthogonal vectors in each base. We study the mutual information between the legitimate parties and the eavesdropper and the error rate by considering various incoherent eavesdropping attacks as a function of the dimension of the Hilbert space.

  • 45. Bourennane, M.
    et al.
    Karlsson, Anders
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Björk, Gunnar
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    Gisin, N.
    Cerf, N. J.
    Quantum key distribution using multilevel encoding: security analysis2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 47, p. 10065-10076Article in journal (Refereed)
    Abstract [en]

    We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N-dimensional Hilbert space. We,estimate both the mutual information between the legitimate parties and the eavesdropper, and the error rate, as a function of the dimension of the Hilbert space. We derive the information gained by an eavesdropper using optimal incoherent attacks and an upper bound on the legitimate party error rate that ensures unconditional security when the eavesdropper uses finite coherent eavesdropping attacks. We also consider realistic systems where we assume that the detector dark count probability is not negligible.

  • 46. Chen, Yuntian
    et al.
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.
    Generation and detection of photonic qutrit states by linear optics2008In: Quantum information & computation, ISSN 1533-7146, Vol. 8, no 5, p. 386-398Article in journal (Refereed)
    Abstract [en]

    We address the problem of generation and detection of the four mutually unbiased biphoton polarization-qutrit bases by linear optics. First, the generation of the bases is studied. Our numeric results show that the linear optics method can be used to generate the 4 mutually unbiased basis qutrit states probabilistically with high fidelity. Second, we investigate whether or not linear polarization-optics components are sufficient to realize the simultaneous detection of the qutrit states forming a complete basis. Analytical results show that every state in two of the bases, namely only half of the 4 mutually unbiased bases qutrit states can be identified.

  • 47. de la Hoz, P.
    et al.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    de Guise, H.
    Klimov, A. B.
    Leuchs, G.
    Sanchez-Soto, L. L.
    Classical polarization multipoles: paraxial versus nonparaxial2015In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 90, no 7, article id 074030Article in journal (Refereed)
    Abstract [en]

    We discuss the polarization of paraxial and nonparaxial classical light fields by resorting to a multipole expansion of the corresponding polarization matrix. It turns out that only a dipolar term contributes when one considers SU(2) (paraxial) or SU(3) (nonparaxial) as fundamental symmetries. In this latter case, one can alternatively expand in SU(2) multipoles, and then both a dipolar and a quadrupolar component contribute, which explains the richer structure of this nonparaxial instance. These multipoles uniquely determine Wigner functions, in terms of which we examine some intriguing hallmarks arising in this classical scenario.

  • 48. de la Hoz, P.
    et al.
    Björk, Gunnar G.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Klimov, A. B.
    Leuchs, G.
    Sanchez-Soto, L. L.
    Unpolarized states and hidden polarization2014In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 90, no 4, p. 043826-Article in journal (Refereed)
    Abstract [en]

    We capitalize on a multipolar expansion of the polarization density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order K vanish, we can properly say that the state is Kth-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of hidden polarization emerges in a natural way in this context.

  • 49. de la Hoz, P.
    et al.
    Klimov, A. B.
    Björk, Gunnar
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Kim, Y. -H
    Müller, C.
    Marquardt, Ch.
    Leuchs, G.
    Sanchez-Soto, L. L.
    Multipolar hierarchy of efficient quantum polarization measures2013In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, no 6, p. 063803-Article in journal (Refereed)
    Abstract [en]

    We advocate a simple multipole expansion of the polarization density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles we construct a whole hierarchy of measures that accurately assess higher-order polarization fluctuations.

  • 50. Diaz, R. G.
    et al.
    Romero, J. L.
    Björk, Gunnar
    KTH, School of Information and Communication Technology (ICT), Microelectronics and Information Technology, IMIT.
    Bourennane, M.
    Certainty relations between local and nonlocal observables2005In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 7Article in journal (Refereed)
    Abstract [en]

    We point out that for an arbitrary number of identical particles, each defined on a Hilbert space of arbitrary dimension, there exists a whole ladder of relations of complementarity between certain local and nonlocal measurements corresponding to every conceivable grouping of the particles, e. g., the more accurately we can know ( by a measurement) some joint property of three qubits ( projecting the state onto a tripartite-entangled state), the less accurate some other property, local to the three qubits, becomes. We investigate the relation between these complementarity relations and a similar relation based on interference visibilities. We also show that the complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.

123 1 - 50 of 120
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