Operational quasiprobabilities for qudits

TL;DR

This paper introduces an operational quasiprobability function for qudits that distinguishes quantum behavior from hidden-variable models through negativity, and demonstrates its use as an entanglement witness and in experiments.

Contribution

It proposes a new quasiprobability framework for qudits that operationally detects nonclassicality and entanglement, extending previous methods with practical experimental implications.

Findings

Negativity indicates nonclassicality and nonlocality.

The quasiprobability function acts as an entanglement witness.

Experimental demonstration with polarization qubits shows nonclassicality.

Abstract

We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results are described by a hidden-variable model with locality and noninvasive measurability assumed. Otherwise, it is negative valued. The negativity depends on the observables to be measured as well as a given state, as the quasiprobability function is operationally defined. We also propose a marginal quasiprobability function and show that it plays the role of an entanglement witness for two qudits. In addition, we discuss an optical experiment of a polarization qubit to demonstrate its nonclassicality in terms of the quasiprobability function.