Adaptive Channel Reshaping for Improved Entanglement Distillation

TL;DR

This paper introduces adaptive channel reshaping protocols that significantly improve entanglement distillation rates for noisy quantum channels, providing new bounds and insights for quantum communication efficiency.

Contribution

It presents novel adaptive and recurrent distillation protocols that reshape noisy channels into more favorable ones, surpassing previous rate bounds for amplitude damping and depolarizing channels.

Findings

Reshaping channels into erasure channels exceeds previous bounds.

Greedy recurrence protocol improves distillation rates for depolarizing channels.

New bounds enhance understanding of quantum information processing.

Abstract

Quantum communication and computation heavily rely on entanglement distillation protocols. There is a plethora of distillation protocols for Pauli channels and also for some non-Pauli channels. However, an effort to relate the effectiveness of these protocols has been missing. For most quantum channels, the gap between the existing lower and upper bounds on distillation rates is substantial, and improvements of achievable rates have been stagnant for decades. In this work, we improve the best known distillation lower bounds, for both the amplitude damping and depolarizing channels. We build on a key observation that distillation protocols reshape several uses of a very noisy channel into a better effective channel. We apply this channel processing in an adaptive and recurrent manner. For the amplitude damping channel, our suggested protocol reshapes the channel into an erasure channel, achieving rates exceeding the best known lower bound given by the channel's reverse coherent information. For the depolarizing channel, we introduce the Greedy recurrence protocol with proven performance guarantees and construct a combined protocol improving upon previously known distillation rates. Improved bounds on attainable distillation rates give insights for both practical implementations and theoretical understanding of quantum information processing.