Measuring quantumness via anticommutators

TL;DR

This paper presents a novel method to detect the quantumness of a system by analyzing the sign of the anticommutator of two states, highlighting a fundamental difference from classical states.

Contribution

The paper introduces a new approach to witness quantumness using anticommutators, emphasizing their positivity in classical states and potential negativity in quantum states.

Findings

Anticommutators of classical states are always positive.

Quantum states can produce nonpositive anticommutators.

Interference relates to the trace of the anticommutator.

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.