Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes

TL;DR

This paper improves the upper bounds on the quantum capacity of Gaussian loss channels and demonstrates that Gottesman-Kitaev-Preskill codes can nearly achieve these capacities, with practical optimization methods identifying GKP codes as optimal encodings.

Contribution

It provides tighter capacity bounds for Gaussian loss channels and shows GKP codes are near-optimal, including an optimization approach for energy-constrained scenarios.

Findings

GKP codes achieve near the quantum capacity of Gaussian loss channels.

New upper bounds on channel capacity are established.

Numerical optimization identifies GKP codes as optimal encodings.

Abstract

Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide improved upper bounds of Gaussian loss channel capacity, both in the energy-constrained and unconstrained scenarios. We briefly review the Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energy-unconstrained case, that the GKP codes achieve the quantum capacity of Gaussian loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize the entanglement fidelity. The biconvex optimization is solved by an alternating semidefinite programming (SDP) method and we report that, starting from random initial codes, our numerical optimization yields GKP codes as the optimal encoding in a practically relevant regime.