Post-measurement quantumness. (11th November 2021)

• Record Type: Journal Article
• Authors: Sun, Yuan; Luo, Shunlong
• Is Part Of: Physica scripta. Volume 96:Number 12(2021)
• Publication Date: 2021-11-11
• Subjects: measurement -- ensemble -- Gram matrix -- coherence -- quantumness; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/ac34b5
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: A quantum measurement (e.g., positive-operator valued measure, or more generally, instrument) performed on a system state yields a post-measurement ensemble (a family of outcome states together with the corresponding outcome probabilities), which may have quantumness due to the impossibility to perfectly discriminate the constituent states. In order to characterize information contents and structure of a measurement, it is desirable to investigate the post-measurement ensemble. In this work, we study post-measurement quantumness (i.e., quantumness of the post-measurement ensemble) by introducing a Gram matrix summarizing the interaction between a measurement and a state, and explore its implications and consequences. Gram matrix of an ensemble can be regarded as a quantum state (density operator) in an auxiliary system with a computational basis labelling the measurement outcomes. Our basic idea is to exploit coherence of the Gram matrix (with respect to the computational basis of the auxiliary system) and employ it to quantify post-measurement quantumness . We propose several quantifiers of quantumness and reveal their basic properties. We further evaluate explicitly quantumness of measurements arising from several important quantum channels, and illustrate a comparison between them. This provides a method for investigating measurements from the perspective of coherence of Gram matrix.