Entanglement-of-formation potentials for feedback-assisted classical communication and randomness distillation

2026-10-04

AI Summary

This study addresses the unresolved bounds on classical communication capacity and one-way randomness distillation for quantum channels lacking shared entanglement. To this end, it proposes a unified entanglement-based framework that introduces the entanglement formation potential. By integrating mixed convex roof expressions, weak measurement protocols, and Choi state analysis, the authors derive exact amortization theorems to bound the classical feedback capacity. The work demonstrates that preserving quantum correlations enables two-way distillation to surpass one-way limits, thereby refining established channel bounds. Furthermore, it determines capacities for specific noisy channels, strengthens converse theorems for depolarizing channels, and provides exact benchmarks alongside finite blocklength upper bounds for amplitude damping channels.

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.

Problem

• feedback-assisted classical communication
• randomness distillation
• entanglement-of-formation potentials
• quantum channel capacity
• finite-blocklength bounds

Innovation

• entanglement-of-formation potentials
• feedback-assisted classical communication
• randomness distillation
• amortization theorem
• weak-measurement protocol