Defining quantumness via the Jordan product

Abstract

We propose alternative definitions of classical states and quantumness witnesses by focusing on the algebra of observables of the system. A central role will be assumed by the anticommutator of the observables, namely the Jordan product. This approach turns out to be suitable for generalizations to infinite dimensional systems. We then show that the whole algebra of observables can be generated by three elements by repeated application of the Jordan product.

References in corpus (7)

• Experimental test of nonclassicality for a single particle
• Reduction of Lie-Jordan Banach algebras and quantum states
• Improved implementation of nonclassicality test for a single particle
• Quantumness tests and witnesses in the tomographic-probability representation
• Quantumness and Entanglement Witnesses
• Measuring quantumness via anticommutators
• Classical to quantum in large number limit

Cited by in corpus (6)

• Anomalous Weak Values and the Violation of a Multiple-measurement Leggett-Garg Inequality
• Detecting non-Markovianity via uncertainty relations
• Measuring quantumness: from theory to observability in interferometric setups
• Parametric models and information geometry on W*-algebras
• Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes