Coherence Scaling in Quantum Communication Protocols

TL;DR

This paper studies how quantum coherence scales in communication protocols, revealing that some protocols like superdense coding can be scalable with limited coherence growth, while teleportation incurs a linear coherence cost.

Contribution

It introduces a circuit-level measure of coherence, analyzes coherence scaling in superdense coding and teleportation, and clarifies the coherence costs and bounds in quantum communication.

Findings

Superdense coding can have logarithmic or constant coherence growth.

Teleportation exhibits a linear coherence cost per teleported qubit.

Intermediate coherence generation is consistent with information-theoretic bounds.

Abstract

We investigate how quantum coherence scales and is redistributed in quantum communication protocols, using superdense coding and quantum teleportation as paradigmatic case studies. Employing the relative entropy of coherence as a circuit-level resource measure, we show that multipartite resource states relevant to generalized superdense coding can enable scalable communication while exhibiting only logarithmic or even constant coherence growth, depending on their entanglement structure. In sharp contrast, quantum teleportation displays an unavoidable, protocol-induced coherence cost that grows linearly with the number of teleported qubits and is independent of the input state. Through a stage-resolved analysis of the teleportation circuit, we separate protocol-generated coherence from message-dependent contributions and identify a universal two-bit coherence offset per teleported qubit at the maximal-coherence stage. We further demonstrate explicitly that this extensive intermediate coherence generation is fully consistent with information-theoretic bounds, including the Holevo limit, and does not correspond to an increase in accessible classical information.