The information capacity of a single photon

TL;DR

This paper investigates the maximum amount of information that can be transmitted using a single photon through an optical fiber, considering spectral encoding and channel properties, and derives bounds and exact capacities.

Contribution

It introduces a theoretical framework for calculating the upper bounds and exact capacity of spectral encoding in single-photon quantum channels.

Findings

Derived analytic bounds on channel capacity.

Calculated exact capacity for symmetric two-state encoding.

Linked spectral encoding basis to channel capacity limits.

Abstract

Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarisation states of single photons has been widely used as these states form an natural closed two state qubit. However, photons are able to encode much more -- in principle infinite -- information via the continuous spatio-temporal degrees of freedom. Here we consider the information capacity of an optical quantum channel, such as an optical fibre, where a spectrally encoded single photon is the means of communication. We use the Holevo bound to calculate an upper bound on the channel capacity, and relate this to the spectral encoding basis and the spectral properties of the channel. Further, we derive analytic bounds on the capacity of such channels, and in the case of a symmetric two-state encoding calculate the exact capacity of the corresponding channel.