Coherence requirements for quantum communication from hybrid circuit dynamics

TL;DR

This paper investigates the coherence requirements for quantum communication and error correction using hybrid circuit dynamics, revealing phase transitions and bounds on code distance related to coherence resources.

Contribution

It introduces a game-theoretic framework to determine coherence thresholds for quantum communication and establishes bounds on error correction code distance based on coherence.

Findings

Identifies coherence-tuned phase transitions in entanglement and channel capacity.

Derives minimum coherence requirements for successful quantum communication strategies.

Proves coherence bounds on the code distance in stabilizer quantum error correction codes.

Abstract

The coherent superposition of quantum states is an important resource for quantum information processing which distinguishes quantum dynamics and information from their classical counterparts. In this article we determine the coherence requirements to communicate quantum information in a broad setting encompassing monitored quantum dynamics and quantum error correction codes. We determine these requirements by considering hybrid circuits that are generated by a quantum information game played between two opponents, Alice and Eve, who compete by applying unitaries and measurements on a fixed number of qubits. Alice applies unitaries in an attempt to maintain quantum channel capacity, while Eve applies measurements in an attempt to destroy it. By limiting the coherence generating or destroying operations available to each opponent, we determine Alice's coherence requirements. When Alice plays a random strategy aimed at mimicking generic monitored quantum dynamics, we discover a coherence-tuned phase transitions in entanglement and quantum channel capacity. We then derive a theorem giving the minimum coherence required by Alice in any successful strategy, and conclude by proving that coherence sets an upper bound on the code distance in any stabelizer quantum error correction codes. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.