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• 1.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
Quantum error correction2016Doctoral thesis, comprehensive summary (Other academic)

Quantum error correction is the art of protecting quantum states from the detrimental influence from the environment. To master this art, one must understand how the system interacts with the environment and gives rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. Such phenomena include decoherence, an effect that in general destroys superpositions of pure states as a consequence of entanglement with the environment. But decoherence can also be understood as “information leakage”, i.e., when knowledge of an encoded code block is transferred to the environment. In this event, the block’s information or entanglement content is typically lost.

In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment “picks up” information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code.

Often, it is assumed that the environment’s ability to distinguish between error events is small, and I will denote such environments “memory-less”. But this assumption is not always valid, since the ability to distinguish error events is related to the temperature of the environment, and in the particular case of information coded onto photons, kBTR «ℏω typically holds, and one must then assume that the environment has a “memory”. In the thesis I describe a short quantum error-correction code adapted for photons interacting with a “cold” reservoir, i.e., a reservoir which continuously probes what error occurred in the coded state.

I also study other types of environments, and show how to distill meaningful figures of merit from codes adapted for these channels, as it turns out that resource-based figures reflecting both information and entanglement can be calculated exactly for a well-studied class of channels: the Pauli channels. Starting from these resource-based figures, I establish the notion of efficiency and quality and show that there will be a trade-off between efficiency and quality for short codes. Finally I show how to incorporate, into these calculations, the choices one has to make when handling quantum states that have been detected as incorrect, but where no prospect of correcting them exists, i.e., so-called detection errors.

• 2.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
Quantum error correction2012Licentiate thesis, comprehensive summary (Other academic)

This thesis intends to familiarise the reader with quantum error correction, and also show some relations to the well known concept of information - and the lesser known quantum information. Quantum information describes how information can be carried by quantum states, and how interaction with other systems give rise to a full set of quantum phenomena, many of which have no correspondence in classical information theory. These phenomena include decoherence, as a consequence of entanglement. Decoherence can also be understood as "information leakage", i.e., knowledge of an event is transferred to the reservoir - an effect that in general destroys superpositions of pure states.

It is possible to protect quantum states (e.g., qubits) from interaction with the environment - but not by amplification or duplication, due to the "no-cloning" theorem. Instead, this is done using coding, non-demolition measurements, and recovery operations. In a typical scenario, however, not all types of destructive events are likely to occur, but only those allowed by the information carrier, the type of interaction with the environment, and how the environment "picks up" information of the error events. These characteristics can be incorporated into a code, i.e., a channel-adapted quantum error-correcting code. Often, it is assumed that the environment's ability to distinguish between error events is small, and I will denote such environments "memory-less".

This assumption is not always valid, since the ability to distinguish error events is related to the \emph{temperature} of the environment, and in the particular case of information coded onto photons, $k_{\text{B}}T_{\text{R}}\ll\hbar\omega$ typically holds, and one must then assume that the environment has a "memory". In this thesis, I describe a short quantum error-correcting code (QECC), adapted for photons interacting with a cold environment, i.e., this code protects from an environment that continuously records which error occurred in the coded quantum state.

Also, it is of interest to compare the performance of different QECCs - But which yardstick should one use? We compare two such figures of merit, namely the quantum mutual information and the quantum fidelity, and show that they can not, in general, be simultaneously maximised in an error correcting procedure. To show this, we have used a five-qubit perfect code, but assumed a channel that only cause bit-flip errors. It appears that quantum mutual information is the better suited yardstick of the two, however more tedious to calculate than quantum fidelity - which is more commonly used.

• 3.
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).
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)
• 4.
KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO.
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)

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.

• 5.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
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)

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.

• 6.
KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
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)
• 7.
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering. KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
Negative permeability in a Lambda-type three-level atomic vapor2007In: Applied Physics A: Materials Science & Processing, ISSN 0947-8396, E-ISSN 1432-0630, Vol. 87, p. 291-295Article in journal (Refereed)

A new approach is suggested to realize negative magnetic permeability that follows directly from quantum mechanics. It is shown that a Delta-type three-level atomic system with proper atomic parameters can give rise to striking magnetic responses, which could exhibit negative permeability in an optical frequency band. Both steady and transient behaviors of the magnetic permeability in the atomic vapor are studied. The present negative-permeability vapor could be mixed with a quantum coherent vapor whose electric permittivity is negative. Such a mixed vapor may give an isotropic left-handed vapor medium at the atomic-scale level.

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