Quantumness Witnesses

TL;DR

This paper broadens the concept of quantumness witnesses, comparing them to entanglement tests, and illustrates their application in single qubits, many-body systems, and phase space representations.

Contribution

It introduces the notion of quantumness witnesses, expanding the framework for testing quantum properties beyond entanglement and Bell inequalities.

Findings

Quantumness witnesses can be constructed for various quantum systems.

Comparison shows different tests detect quantumness in complementary ways.

Phase space-based witnesses offer a new perspective on quantumness detection.

Abstract

A recently proposed test of quantumness [R. Alicki and N. Van Ryn, J. Phys. A: Math. Theor. 41 062001 (2008)] is put into a broader mathematical and physical perspective. The notion of quantumness witness is introduced, in analogy to entanglement witness, and illustrated by examples of a single qubit and many-body systems with additive observables. We compare also our proposal with the quantumness test based on quantum correlations (entanglement) and Bell inequalities. A class of quantumness witnesses associated to the phase space representation is also discussed.