Natural Metric for Quantum Information Theory

Abstract

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.

v2: enlarged; presented at ISIT 2008 (Toronto)

References in corpus (5)

• Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states
• Properties of Classical and Quantum Jensen-Shannon Divergence
• On the metric character of the quantum Jensen-Shannon divergence
• Alternative fidelity measure for quantum states
• Wootters' distance revisited: a new distinguishability criterium

Cited by in corpus (9)

• Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence
• A family of generalized quantum entropies: definition and properties
• Distinguishability of generic quantum states
• Comment on "Improved bounds on entropic uncertainty relations"
• Spin squeezing and entanglement via finite-dimensional discrete phase-space description
• Purification-based metric to measure the distance between quantum states and processes
• Quantum distinguishability measures: projectors vs. states maximization
• Unified scheme for correlations using linear relative entropy
• Distinguishability notion based on Wootters statistical distance: application to discrete maps