Coherence requirements for quantum communication from hybrid circuit dynamics

Kelly, Shane P.; Poschinger, Ulrich; Schmidt-Kaler, Ferdinand; Fisher, Matthew P. A.; Marino, Jamir

doi:10.21468/SciPostPhys.15.6.250

SciPost Physics

Coherence requirements for quantum communication from hybrid circuit dynamics

Shane P. Kelly, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Matthew P. A. Fisher, Jamir Marino

SciPost Phys. 15, 250 (2023) · published 22 December 2023

doi: 10.21468/SciPostPhys.15.6.250
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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 code. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.250
TI  - Coherence requirements for quantum communication from hybrid circuit dynamics
PY  - 2023/12/22
UR  - https://scipost.org/SciPostPhys.15.6.250
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 250
A1  - Kelly, Shane P.
AU  - Poschinger, Ulrich
AU  - Schmidt-Kaler, Ferdinand
AU  - Fisher, Matthew P. A.
AU  - Marino, Jamir
AB  - 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 code. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.
ER  -

@Article{10.21468/SciPostPhys.15.6.250,
	title={{Coherence requirements for quantum communication from hybrid circuit dynamics}},
	author={Shane P. Kelly and Ulrich Poschinger and Ferdinand Schmidt-Kaler and Matthew P. A. Fisher and Jamir Marino},
	journal={SciPost Phys.},
	volume={15},
	pages={250},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.250},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.250},
}

Cited by 8

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¹ ² Shane P. Kelly,
¹ Ulrich Poschinger,
² Ferdinand Schmidt-Kaler,
¹ Matthew P. A. Fisher,
¹ ² Jamir Marino

Funders for the research work leading to this publication