Efficient capacity-achieving entanglement generation with application to pure-loss Bosonic channels

2026-10-02

AI Summary

This study addresses the lack of efficient capacity-approaching coding schemes for quantum systems such as the pure-loss bosonic channel by proposing an entanglement generation protocol based on polar codes. Methodologically, it integrates classical polar decoding with the belief propagation with quantum messages (BPQM) algorithm to construct the first quantum communication protocol supporting explicit and efficient decoding. The proposed scheme maximizes coherent information over degradable and specific classical-quantum channels. Furthermore, it achieves, for the first time, the theoretical quantum capacity limit of the pure-loss bosonic channel under energy constraints. By providing a highly efficient coding paradigm, this work offers a critical advancement for continuous-variable quantum communication.

Abstract

While the ultimate limits on the rate of quantum communication over noisy channels are well-established, very few efficient coding schemes achieving these limits are known. This contrasts sharply with transmitting classical data over classical channels, where polar codes and low-density parity-check codes both efficiently achieve the classical capacity of any noisy channel. In this work we construct an efficient entanglement generation scheme which achieves the coherent information for a broad class of channels. For degradable channels in the class, which includes truncated versions of the pure loss Bosonic channel, the resulting scheme achieves the quantum capacity. The construction makes use of polar codes for two kinds of classical-input, quantum-output (CQ) channels: those with commuting outputs and those whose outputs are heralded mixtures of pure states. The former case is amenable to decoding by classical polar decoding algorithms, the latter by the belief propagation with quantum messages (BPQM) algorithm. To our knowledge, this construction is the first explicit and efficiently decodable protocol that achieves the energy-constrained quantum capacity of the pure-loss Bosonic channel.

Problem

• quantum capacity
• entanglement generation
• pure-loss Bosonic channel
• polar codes
• efficient coding scheme

Innovation

• entanglement generation
• polar codes
• pure-loss Bosonic channel
• quantum capacity
• BPQM