Covert Entanglement Generation over Bosonic Channels

TL;DR

This paper demonstrates that it is possible to covertly generate a significant amount of entanglement over bosonic channels using a square root law, with practical considerations for implementation.

Contribution

It establishes a square root law for covert entanglement generation over bosonic channels and provides a single-letter expression for optimal entanglement rate.

Findings

Square root law applies to covert entanglement generation.

Single-letter expression for optimal entanglement rate derived.

Analysis of practical photonic qubit implementations included.

Abstract

We explore covert entanglement generation over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical settings, including optical, microwave, and radio-frequency (RF) channels. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We show that a square root law (SRL) for covert entanglement generation similar to that for classical communication: $L_{\rm EG}\sqrt{n}$ entangled bits (ebits) can be generated covertly and reliably over $n$ uses of a bosonic channel. We report a single-letter expression for optimal $L_{\rm EG}$ as well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits, which may be more practical for physical implementation.