Strong limits proven for quantum data loss over pure-loss channels
Strong converse for the quantum capacity of the pure-loss bosonic channel
Information Theory
Summary
This paper proves a strong limit on how much quantum information can be reliably sent over certain types of noisy channels called pure-loss bosonic channels. Specifically, it shows that any attempt to communicate quantum information at a rate above the channel’s capacity will fail with very high probability as the number of channel uses grows. The authors’ proof works without needing limits on input energy and applies to the most general encoding and decoding schemes. Their techniques combine new mathematical bounds on quantum information measures with insights about light splitting in these channels.
What this means in practice
- •For quantum communication engineers: Set fundamental performance limits and failure rates when designing quantum networks that use optical fiber or free-space channels modeled as pure-loss bosonic channels.
- •For quantum hardware designers: Guide hardware development by clarifying how channel loss constraints impact achievable quantum data transmission rates without energy restrictions.
A theory result. No direct application yet.
Authors
Mark M. Wilde
Abstract
This paper reports the proof of a strong converse for the unconstrained quantum capacity of the pure-loss bosonic channel. At every fixed rate above capacity, the entanglement-generation fidelity of every code is bounded by a constant times the reciprocal of the number of channel uses. The bound holds without an energy constraint and for arbitrary encoded states, including states correlated across all input modes, and arbitrary joint decoders. The proof combines quantum Chebyshev and hockey-stick testing inequalities with a uniform relative-entropy-variance bound for the balanced pure-loss channel, corresponding to transmissivity $η=1/2$. The variance bound follows by expressing the balanced beam splitter in bright and dark modes: the dark modes are exactly in vacuum, and any state orthogonal to that vacuum contains at least one dark photon. For general transmissivity, dilating the degrading attenuator reduces the problem to this balanced-channel setting and bounds the decoder test by precisely the factor that produces the known quantum-capacity threshold. The resulting argument establishes the strong converse at the unconstrained quantum capacity for every pure-loss bosonic channel.