Measuring quantumness via anticommutators

Abstract

We introduce a method to witness the quantumness of a system. The method relies on the fact that the anticommutator of two classical states is always positive. We show that there is always a nonpositive anticommutator due to any two quantum states. We notice that interference depends on the trace of the anticommutator of two states and it is therefore more natural to detect quantumness by looking at anticommutators of states rather than their commutators.

7 pages, 2 figures

References in corpus (8)

• The classical-quantum boundary for correlations: discord and related measures
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Detecting Multipartite Classical States and their Resemblances
• Experimental test of nonclassicality for a single particle
• Quantumness Witnesses
• Improved implementation of nonclassicality test for a single particle
• Quantumness and Entanglement Witnesses
• Classical to quantum in large number limit

Cited by in corpus (5)

• Measuring quantumness: from theory to observability in interferometric setups
• Defining quantumness via the Jordan product
• Identifying quantumness via addition-then-subtraction operation
• Quantifying Nonclassicality of Correlations based on the Concept of Nondisruptive Local State Identification
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes