Negativity of Wigner distribution function as a measure of incompatibility

• URL: http://arxiv.org/abs/2306.07917v1
• Date: Tue, 13 Jun 2023 17:22:56 GMT
• Title: Negativity of Wigner distribution function as a measure of incompatibility
• Authors: Jatin Ghai, Gautam Sharma and Sibasish Ghosh
• Abstract summary: Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. We establish a connection between the negativity of the Wigner function, a well-known phase-space quasiprobability distribution, of finite-dimensional Hermitian operators and incompatibility among them. We generalize our treatment for higher dimensional qudits for specific finite-dimensional Gell-Mann operators to observe that with an increase in the dimension of the operators, the negativity of their Wigner distribution, and hence incompatibility, decreases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. Both of them are widely accepted resources in quantum information processing. We acquaint an approach to establish a connection between the negativity of the Wigner function, a well-known phase-space quasiprobability distribution, of finite-dimensional Hermitian operators and incompatibility among them. We calculate the negativity of the Wigner distribution function for noisy eigenprojectors of qubit Pauli operators as a function of the noise and observe that the amount of negativity increases with the decrease in noise vis-\`a-vis the increase in the incompatibility. It becomes maximum for the set of maximally unbiased operators. Our results, although qualitatively, provide a direct comparison between relative degrees of incompatibility among a set of operators for different amounts of noise. We generalize our treatment for higher dimensional qudits for specific finite-dimensional Gell-Mann operators to observe that with an increase in the dimension of the operators, the negativity of their Wigner distribution, and hence incompatibility, decreases.

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