Quantifying Margenau--Hill Nonclassicality
Abstract
Quasiprobability distributions offer a useful way of describing nonclassical features of quantum systems through their departure from classical probability theory. In this work, we investigate the quantification of nonclassicality associated with the Margenau--Hill quasiprobability (MHQ) distribution using its moments, without requiring reconstruction of the full distribution. First we introduce the logarithmic MHQ negativity as a quantifier of nonclassicality, and then derive a hierarchy of rigorous lower bounds in terms of low-order moments. Within the resulting hierarchy, the fourth-moment bound is the strongest among the bounds based on even moments. For qubits, we further derive a tight upper bound on the exact MHQ negativity and identify the corresponding extremal state. We also obtain an optimal positivity threshold based on the fourth moment for arbitrary pairs of qubit observables. Finally, we show that the relevant moments admit exact multicopy representations, providing a route to their estimation using interferometry or classical shadow techniques. Our results establish a moment-based framework for extracting quantitative information about MHQ negativity from a finite set of low-order observables.
Related
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- Nonclassicality of a macroscopic qubit-ensemble via parity measurement induced disturbance
- Tsirelson's nonclassicality witness under dissipative dynamics
- Nonclassicality from Incomplete Fock-State Statistics
- Fock-state filtering of squeezed states: enhanced nonclassicality and effects of a thermal bath
BibTeX
@misc{chakrabarty2026quantifying,
title = {{Quantifying Margenau--Hill Nonclassicality}},
author = {Sudip Chakrabarty},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07869},
eprint = {2609.07869},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07869},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantifying Margenau--Hill Nonclassicality
AU - Sudip Chakrabarty
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07869
UR - https://arxiv.org/abs/2609.07869
AB - Quasiprobability distributions offer a useful way of describing nonclassical features of quantum systems through their departure from classical probability theory. In this work, we investigate the quantification of nonclassicality associated with the Margenau--Hill quasiprobability (MHQ) distribution using its moments, without requiring reconstruction of the full distribution. First we introduce the logarithmic MHQ negativity as a quantifier of nonclassicality, and then derive a hierarchy of rigorous lower bounds in terms of low-order moments. Within the resulting hierarchy, the fourth-moment bound is the strongest among the bounds based on even moments. For qubits, we further derive a tight upper bound on the exact MHQ negativity and identify the corresponding extremal state. We also obtain an optimal positivity threshold based on the fourth moment for arbitrary pairs of qubit observables. Finally, we show that the relevant moments admit exact multicopy representations, providing a route to their estimation using interferometry or classical shadow techniques. Our results establish a moment-based framework for extracting quantitative information about MHQ negativity from a finite set of low-order observables.
ER -