Attaining classical capacity per unit cost of noisy bosonic Gaussian channels

Marcin Jarzyna

doi:10.1103/physreva.104.022605

Marcin Jarzyna

Open Access

https://doi.org/10.1103/physreva.104.022605

Copy DOI

Abstract

I show that classical capacity per unit cost of noisy bosonic Gaussian channels can be attained by employing a generalized on-off keying modulation format and a projective measurement of individual output states. This means that neither complicated collective measurements nor phase-sensitive detection is required to communicate over optical channels at the ultimate limit imposed by laws of quantum mechanics in the limit of low average cost.

Highlights

I show that classical capacity per unit cost of noisy bosonic Gaussian channels can be attained by employing a generalized on-off keying modulation format and a projective measurement of individual output states
The difference is of a qualitative nature as conventional phase-sensitive detection schemes allow for rates scaling linearly with the average number of photons per time bin ∼na in the small-na regime, whereas classical capacity scales as 1 na in the leading order
This discrepancy is even more evident when one looks at the capacity per unit cost (CPC), which quantifies the maximum amount of information that can be transmitted per single photon for a particular protocol, i.e., assuming a certain modulation and detection scheme [7]

Summary

MARCIN JARZYNA

[16], in which it was shown respectively that binary or pulse position modulation formats are enough; the optimal positive operator valued measures (POVMs) were found either only in the trivial case of the noiseless channel or were collective. One obtains the classical capacity per unit cost (CCPC) Cquant which quantifies the best possible PIE attainable for a given quantum channel [15,16] and is equal to Cquant max ρ=|0 0|. Both CPC and CCPC are attained in the limit of vanishing average cost per channel use, na → 0 [7,15,16]. For input in a coherent state with amplitude α the output of the fiducial channel of a general single-mode Gaussian channel is given by a density matrix ρ = D ( |η|α)S(r)ρnbS†(r)D †( |η|α),. Nbk k=0 (nb+1)k+1 k| is a thermal state with the average energy nb and I have chosen the phase of α such that the state is aligned with the position quadrature

The order of the squeezing and displacement operators in

Cost of output signal state