On quantumness in multi-parameter quantum estimation. (4th September 2019)

• Record Type: Journal Article
• Authors: Carollo, Angelo; Spagnolo, Bernardo; Dubkov, Alexander A; Valenti, Davide
• Is Part Of: Journal of statistical mechanics. (2019:Sep.)
• Publication Date: 2019-09-04
• Subjects: 2 -- 11; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab3ccb
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann curvature and the Fisher information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér–Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.