We present a new test of non-randomness that tests both the lower and the upper critical limit of a chi 2-statistic. While checking the upper critical value has been employed by other tests, we argue that also the lower critical value should be examined for non-randomness. To this end, we prepare a binary sequence where all possible bit strings of a certain length occurs the same number of times and demonstrate that such sequences pass a well-known suite of tests for non-randomness. We show that such sequences can be compressed, and therefore are somewhat predictable and thus not fully random. The presented test can detect such non-randomness, and its novelty rests on analysing fixed-length bit string frequencies that lie closer to the a priori probabilities than could be expected by chance alone.

Open-access, online quantum computers have shown significant improvements in the past decade. Although they still suffer from noise and scalability limitations, they do offer the possibility of experimenting with quantum circuits which would otherwise have required laboratory resources and prowesses beyond the reach of most students (and even researchers). In view of this, we revisit from the ground up the notion of contextuality and show that it can now be easily demonstrated on one of the IBM quantum computers. We showcase this with an implementation of the Peres-Mermin square which, despite the high error rates, manages to violate noncontextuality by almost 28 standard deviations.

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincare sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincare space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.

The files contain randomly-ordered N-number system elements where N=13,16,17, 24 and 25. For N=24, two such sequences were concatenated (each with a different random order).

We investigate the minimum acquisition time, expressed as the number of image frames, and the minimum number of absorbed photons per pixel required to achieve a predefined contrast resolution in a monochromatic, pixelated image acquisition system at low light intensities (from well below one photon, to several hundred photons per pixel and frame). Primarily we compare systems based on the pixels of the photon-number-resolving (PNR) type of detectors and detectors that discriminate, in a binary fashion, between zero and non-zero photon numbers (so-called click detectors). We find that our model can seamlessly interpolate between the two. We also model detectors with intrinsic PNR capabilities and integrating detectors with a simple saturation model, derive the probability of errors in assigning the correct intensity (or ‘gray level’) and finally discuss how the estimated levels, which need to be based on threshold levels due to the stochastic nature of the detected photon number, should be assigned. Overall, we find that non-ideal PNR-detector-based systems offer advantages even over ideal click-detector-based systems when the incident mean photon number is sufficiently large, which is guaranteed to occur around ten photons per pixel and frame.

We derive a computationally efficient expression of the photon-counting distribution for a uniformly illuminated array of single-photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of an ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a handful of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters, and we compute the optimal size of the array that yields the smallest error.

We present an experimental realization of a 16 element, temporal-array, photon-number-resolving (PNR) detector, which is a multiplexed single-photon detector that splits an input signal over multiple time bins, and the time bins are detected using two superconducting nanowire single-photon detectors (SNSPD). A theoretical investigation of the PNR capabilities of the detector is performed and it is concluded that, compared to a single-photon detector, our array detector can resolve one order of magnitude higher mean photon numbers, given the same number of input pulses to measure. This claim is experimentally verified and we show that the detector can accurately predict photon numbers between 10(-3) and 10(2). Our present detector is incapable of single-shot photon-number measurements with high precision since its effective quantum efficiency is 49%. Using SNSPDs with a higher quantum efficiency the PNR performance will improve, but the photon-number resolution will still be limited by the array size.

We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-numberresolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon "click detectors" is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.

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.

For light-intensity-correlation measurements, different methods are used in the high-photon-number or high-intensity regime and in the single- and two-photon regime. Hence, there is an unfortunate measurement "gap" primarily for multiphoton, quantum states. These states, for example, multiphoton Fock states, will be increasingly important in the realization of quantum technologies and in exploring the boundaries between quantum and classical optics. We show that a naive approach based on attenuation, state splitting, and two-detector correlation can give the correct two-time intensity correlation for any state. We analyze how added losses decrease the measurement systematic error. The price to be paid is that the losses increase the measurement statistical error or, alternatively, increase the acquisition time for a given tolerable level of statistical error. We have experimentally demonstrated the feasibility of the method for a coherent state and a quasithermal state. The method is easy to implement in any laboratory and will simplify characterization of medium and highly excited nonclassical states as they become experimentally available.