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Journal of the Optical Society of America B

Distortion of photon-correlation functions in detection systems with paralyzable dead-time effects

Vladimir V. Apanasovich, Sergey Paltsev

Published Sep 1, 1995• 7 citations
Publisher

Abstract

We introduce an analytical model of the influence of paralyzable dead time on registered photon-correlation functions. Distortions of correlation functions in the case of the Poisson point process, the doubly stochastic Poisson point process, and the pairwise point process are calculated. The model permits the analysis of detection systems with constant and random dead times. The results of the analytical model are tested by computer simulation.

DOI
10.1364/josab.12.001550

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We introduce an analytical model of the influence of paralyzable dead time on registered photon-correlation functions. Distortions of correlation functions in the case of the Poisson point process, the doubly stochastic Poisson point process, and the pairwise point process are calculated. The model permits the analysis of detection systems with constant and random dead times. The results of the analytical model are tested by computer simulation.
We consider a photonic communication system wherein the photon detector suffers a random ‘dead time’ following each successful photon detection. If subsequent photon arrivals occur during the dead time, the information contained in the photons is assumed to be erased. We refer to such channels as photonic erasure channels and derive fundamental limits on the rate at which classical information can be transmitted on such channels. We assume photon arrivals according to a Poisson process, and consider two classes of detectors - paralyzable and nonparalyzable. We derive explicit expressions for the capacity of photonic erasure channels, for any general distribution of the dead times of the detector. For a photonic erasure channel with a nonparalyzable detector, we show that the capacity depends only on the expected dead time. On the other hand, with a paralyzable detector, the channel capacity depends on the dead time distribution through its Laplace transform.
The paper deals with the modifications in photocount distributions due to dead-time following every registered count. In order to study the effects due to dead-time, the distribution of the interval between successive photocounts is studied. For the case of a constant dead-time, the mean count rate is derived using the dead-time neglected two-fold counting generating function. The result is also generalised to cover the case when the dead-time has a distribution with the different dead-times independently and identically distributed. In view of the complexity of the problem, a lower bound is obtained for the mean square number of photocounts in an arbitrary interval.
Abstract In the case of quantum random number generators based on single photon arrivals, the physical properties of single-photon detectors, such as time-tagger clocks and dead time, influence the stochastic properties of the generated random numbers. This can lead to unwanted correlations among consecutive samples. We present a method based on extending the insensitive periods after photon detections. This method eliminates the unwanted stochastic effects at the cost of reduced generation speed. We calculate performance measures for our presented method and verify its correctness with computer simulations and measurements conducted on an experimental setup. Our algorithm has low complexity, making it convenient to implement in QRNG schemes, where the benefits of having uncorrelated output intervals exceed the disadvantages of the decreased rate.
Recent advances in quantum key distribution (QKD) have given rise to systems that operate at transmission periods significantly shorter than the dead times of their component single-photon detectors. As systems continue to increase in transmission rate, security concerns associated with detector dead times can limit the production rate of sifted bits. We present a model of high-speed QKD in this limit that identifies an optimum transmission rate for a system with given link loss and detector response characteristics.
A quantum random number generation method based on measuring the time differences between photon detections is analyzed mathematically in terms of bit generation efficiency and bit generation rate. It was found that these two values cannot be maximized simultaneously by altering the incident photon rate of a light source with Poisson statistics, but the generation rate can be increased at the expense of efficiency. Analytical results are presented for both an idealized and a practical case. The detector’s dead time has been taken into consideration in the latter case, implying that, for certain combinations of the dead time and the measurement clock period, the generation rate becomes a two-peaked function of the incident photon rate. The theoretical results are confirmed by simulations, showing excellent agreement between the two.
Abstract Using numerical simulation methods that take into account the dead time effect, algorithms are developed to calculate the detector’s response for photon fluxes with different photon number distributions, including the Poisson, Fock, and thermal distributions. Based on the results obtained, a detector tomography method is developed, as well as an algorithm for identifying the corresponding elements of a positive operator-valued measure (POVM). Experimental studies using coherent states demonstrate close agreement between the calculation results and experimental data.