On the consistency of measurement protocols for quantum processes fluctuations

TL;DR

This paper establishes a foundational framework for measuring quantum process fluctuations, identifying a unique protocol that satisfies key physical criteria, thereby enabling consistent fluctuation analysis and extending quantum information concepts to processes.

Contribution

It introduces four fundamental criteria for measuring quantum process fluctuations and proves that only the two-times quantum observables protocol meets all these criteria.

Findings

Only the two-times quantum observables protocol satisfies all criteria.

The framework can resolve inconsistencies in quantum fluctuation measurements.

Enables extension of quantum information concepts to processes.

Abstract

Quantum fluctuations are fundamental in quantum technologies, affecting computing, sensing, cryptography, and thermodynamics. These include fluctuations in the variation of energy, charge, and other observables driven by interactions with lasers and baths. Despite the precise rules quantum mechanics provides for measuring observables at instants of time, no standard framework exists for characterizing the fluctuations of their variations over time. This gap leads to inconsistencies in fluctuation predictions, impacting quantum technologies. In this work, we propose four basic criteria that any measurement of these variations must satisfy, grounded in conservation laws, the no-signaling principle, and expected constraints on physical realism. We demonstrate that only one protocol fulfills all these criteria: the two-times quantum observables. This result has the potential to establish the foundations for measurements of quantum processes, possibly resolving ambiguities in quantum fluctuation measurements. Moreover, it enables the extension of quantum information concepts, such as entanglement and Bell's inequalities, to processes rather than instantaneous observables.