Probability representation and quantumness tests for qudits and two-mode light states

TL;DR

This paper introduces a probability-based method to test the quantum nature of qudits and two-mode light states, using tomographic representations and a quantumness witness to distinguish quantum from classical behaviors.

Contribution

It presents an explicit formula for quantumness witness applicable to qudits and extends the approach to two-mode light states via Jordan-Schwinger map.

Findings

Negative average value of the quantumness witness indicates non-classical behavior.

Comparison of quantum and classical probability representations highlights differences in quantumness.

Method provides a practical way to verify quantumness in high-dimensional systems.

Abstract

Using tomographic-probability representation of spin states, quantum behavior of qudits is examined. For a general j-qudit state we propose an explicit formula of quantumness witnetness whose negative average value is incompatible with classical statistical model. Probability representations of quantum and classical (2j+1)-level systems are compared within the framework of quantumness tests. Trough employing Jordan-Schwinger map the method is extended to check quantumness of two-mode light states.