Entanglement limits one-way quantum communication and randomness rates
Entanglement-of-formation potentials for feedback-assisted classical communication and randomness distillation
Information Theory
Summary
Sending information or creating shared randomness using quantum systems can be helped by feedback and entanglement, but understanding exact limits is tricky. The authors develop new mathematical tools called entanglement-of-formation potentials to precisely bound these limits when only one-way communication or feedback is allowed. They show cases where two-way communication can outperform one-way methods thanks to retained quantum correlations. Their work connects communication and randomness tasks through shared quantum resources and provides benchmarks for channels like the amplitude damping channel.
What this means in practice
- •For quantum communication engineers: Design quantum communication systems with accurate limits on classical data transmission using feedback and entanglement constraints.
- •For quantum cryptography developers: Optimize one-way randomness extraction protocols with tighter bounds for secure key generation under realistic channel noise.
Authors
Mark M. Wilde
Abstract
We develop entanglement-of-formation potentials for feedback-assisted classical communication and one-way randomness distillation. For a finite-dimensional quantum channel without initial shared entanglement, an exact amortization theorem bounds the increase of message information plus entanglement remaining across the communicating laboratories. This proves a classical-feedback capacity bound using a mixed-convex-roof expression previously studied by Winter and Yang in the context of potential capacities. We determine the capacity of flagged mixtures of noiseless and entanglement-breaking channels, improve a published depolarizing-channel converse, and evaluate the new bound exactly for the amplitude damping channel. A state analogue gives a finite-blocklength upper bound on the net shared randomness obtainable with one-way classical communication. Amplitude-damping Choi states provide exact benchmarks, while a full-rank generalized amplitude-damping Choi state demonstrates a useful improvement where we do not evaluate the operational rate exactly. We also distinguish one-way from two-way randomness distillation: a two-round weak-measurement protocol strictly exceeds the exact one-way rate of every nontrivial qubit isotropic state. The protocol preserves quantum side information during its first decoding and extracts additional randomness in the reverse direction. This shows why the one-way state potential is not a general two-way converse. Together, these results establish a common entanglement-based approach to sharper communication and randomness bounds, while revealing how retained quantum correlations enable two-way distillation to surpass one-way limits.