Qubit-portraits of qudit states and quantum correlations

TL;DR

This paper explores qubit-portraits of qudit states to analyze quantum correlations, using a tomographic approach to interpret Bell-like inequalities as classical probability properties, and demonstrates detection capabilities for certain qutrit states.

Contribution

It extends the qubit-portraits framework to characterize quantum correlations in bipartite qudit states, providing new insights into Bell inequality violations.

Findings

Quantum correlations in qutrit isotropic states can be detected.

The method cannot detect correlations in qutrit Werner states.

Bell-like inequalities are interpreted as classical probability properties.

Abstract

The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.