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Coherence requirements for quantum communication from hybrid circuit dynamics
by Shane P. Kelly, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Matthew P. A. Fisher, Jamir Marino
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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.
Published as SciPost Phys. 15, 250 (2023)
Author comments upon resubmission
We appreciate the referees for their careful reading, their comments, and their positive assessment of our manuscript. We have considered the comments by the referees, clarified the relevant points in our manuscript and responded to the their concerns in the referee response section. Our list of changes are viewable there.
Shane P. Kelly, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Matthew P.A. Fisher, Jamir Marino
Submission & Refereeing History
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