Abstract
We calculate numerically the capacity of a lossy photon channel assuming photon number resolving detection at the output. We consider scenarios of input Fock and coherent states ensembles and show that the latter always exhibits worse performance than the former. We obtain capacity of a discrete-time Poisson channel as a limiting behavior of the Fock states ensemble capacity. We show also that in the regime of a moderate number of photons and low losses the Fock states ensemble with direct detection is beneficial with respect to capacity limits achievable with quadrature detection.
Highlights
E VERY communication protocol is carried out by performing physical measurements on physical objects which are fundamentally described by the laws of quantum mechanics
In this paper we investigate the capacity of a lossy optical channel without any kind of additive noise with photon number resolving (PNR) detection at the output which together forms a so-called lossy photon channel
Because of the connection between the Fock state ensemble and the discrete-time Poisson channel in the limit of low transmission and large average number of photons, our findings may allow to increase the performance of communication in various instances in which one can model transmission by the discrete-time Poisson channel, like for example in long range space optical links [44], [45]
Summary
E VERY communication protocol is carried out by performing physical measurements on physical objects which are fundamentally described by the laws of quantum mechanics. Even though the optimal ensembles of quantum states saturating the classical capacity bound for Gaussian channels have been discovered, the necessary measurement schemes remain largely unknown, with the exception of a few particular scenarios [7]–[9]. These involve regimes of very weak and very strong signal strengths, quantified by the average number of photons per channel use Manuscript received January 7, 2021; revised April 9, 2021; accepted April 15, 2021. We show that the capacity attainable with the Fock states ensemble in the limit of low channel transmission while keeping the received average number of photons constant is equal to the capacity of a discrete-time Poisson channel with the optimal prior distributions being the same for both types of channels
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