Quantumness tests and witnesses in the tomographic-probability representation

TL;DR

This paper explores quantumness tests and witnesses within the tomographic-probability framework, introducing parameter-dependent witnesses for qubits and demonstrating their properties using spin tomograms and classical probability relations.

Contribution

It introduces a new family of parameter-dependent quantumness witnesses for qubits within the tomographic-probability representation.

Findings

Parameter-dependent quantumness witnesses are effective for qubits.

Test inequalities relate to standard probability theory.

Spin tomogram analysis supports the validity of the witnesses.

Abstract

In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed in [Alicki and Van Ryn 2008 J. Phys. A: Math. Theor. 41 062001]. For qubits we introduce a general family of quantumness witnesses which are operators depending on an extra parameter. Spin tomogram and dual spin tomographic symbols are used to study qubit examples and the test inequalities which are shown to satisfy simple relations within the framework of the standard probability theory.