Quantum communication over bandwidth-and-time-limited channels

TL;DR

This paper analyzes quantum communication over channels limited by both bandwidth and time, deriving optimal encoding strategies and revealing how channel activation depends on signal duration.

Contribution

It provides analytical solutions for optimal modes in pure-loss bosonic channels with Lorentzian and box spectra, addressing realistic quantum communication constraints.

Findings

Sequential activation of quantum channels with increasing signal duration

Existence of an optimal signal length for limited channel use

Analytical and numerical solutions for various transmission spectra

Abstract

Standard communication systems have transmission spectra that characterize their ability to perform frequency multiplexing over a finite bandwidth. Realistic quantum signals in quantum communication systems like transducers are inherently limited in time due to intrinsic decoherence and finite latency, which hinders the direct implementation of frequency-multiplexed encoding. We investigate quantum channel capacities for bandwidth-and-time-limited (BTL) channels to establish the optimal communication strategy in a realistic setting. For pure-loss bosonic channels, we derive analytical solutions of the optimal encoding and decoding modes for Lorentzian and box transmission spectra, along with numerical solutions for various other transmissions. Our findings reveal a general feature of sequential activation of quantum channels as the input signal duration increases, as well as the existence of optimal signal length for scenarios where only a limited number of channels are in use.