Stochastic resonance in Gaussian quantum channels

TL;DR

This paper investigates the conditions under which stochastic resonance occurs in Gaussian quantum channels, demonstrating its presence in various communication scenarios and highlighting the role of noise and threshold settings.

Contribution

It provides a comprehensive analysis of stochastic resonance in lossy bosonic channels, including classical, entanglement-assisted, and private communication, revealing new effects related to noise and threshold configurations.

Findings

Stochastic resonance occurs if and only if the detection threshold is outside a 'forbidden interval'

Adding Gaussian noise does not depend on who introduces it, sender or receiver

In private communication, the 'forbidden interval' may vanish, enabling resonance at any threshold

Abstract

We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a "forbidden interval". We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel, and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qubit over a lossy bosonic channel with a particular encoding and decoding. In all cases, we assume the addition of Gaussian noise to the signal and show that it does not matter who, between sender and receiver, introduces such a noise. Remarkably, different results are obtained when considering a setting for private communication. In this case the symmetry between sender and receiver is broken and the "forbidden interval" may vanish, leading to the occurrence of stochastic resonance effects for any value of the detection threshold.