Quantum capacity and codes for the bosonic loss-dephasing channel

TL;DR

This paper investigates the quantum capacity of the combined bosonic loss-dephasing channel, revealing its non-degradable nature and identifying optimal codes through numerical methods for various error rates.

Contribution

It provides the first detailed analysis of the loss-dephasing channel's capacity and introduces optimized codes, advancing understanding of bosonic qubit error correction.

Findings

Loss-dephasing channel is non-degradable.

Bounds for the channel capacity are established.

Numerical optimization yields optimal codes for different error rates.

Abstract

Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.