Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off

TL;DR

This paper establishes fundamental thermodynamic limits on quantum error correction, linking measurement heat, information gain, and efficiency, and introduces a triple trade-off relation involving fidelity, efficiency, and measurement efficacy.

Contribution

It derives a novel triple trade-off relation in quantum error correction, connecting thermodynamic efficiency, measurement efficacy, and fidelity, with a thermodynamic interpretation of quantum information gain.

Findings

Derived an upper bound on measurement heat in QEC.

Established a second law of thermodynamics for QEC with feedback.

Proved a fundamental triple trade-off between fidelity, efficiency, and measurement efficacy.

Abstract

Quantum error correction (QEC) is a procedure by which the quantum state of a system is protected against a known type of noise, by preemptively adding redundancy to that state. Such a procedure is commonly used in quantum computing when thermal noise is present. Interestingly, thermal noise has also been known to play a central role in quantum thermodynamics (QTD). This fact hints at the applicability of certain QTD statements in the QEC of thermal noise, which has been discussed previously in the context of Maxwell's demon. In this article, we view QEC as a quantum heat engine with a feedback controller (i.e., a demon). We derive an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain, thereby providing the latter with a physical meaning also when it is negative. Further, we derive the second law of thermodynamics in the context of this QEC engine, operating with general quantum measurements. Finally, we show that, under a set of physically motivated assumptions, this leads to a fundamental triple trade-off relation, which implies a trade-off between the maximum achievable fidelity of QEC and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess. A similar trade-off relation occurs for the thermodynamic efficiency of the QEC engine and the efficacy of the quantum measurement used for error identification.