Maximally antiflat fixed-particle-number fermionic states
Abstract
Fermionic Gaussian states are completely characterized by their two-point correlations, making the covariance matrix a natural reference for quantifying non-Gaussian structure. Motivated by fermionic antiflatness, we study its extremal form for pure number-conserving states and ask which states can be maximally antiflat and how they can be constructed. We show that, at fixed particle number, maximal first antiflatness is equivalent to a completely flat one-body reduced density matrix, and we obtain a complete existence classification together with explicit block and cyclic-orbit constructions of all allowed sectors. We then investigate the structure that appears beyond the covariance level. Maximally antiflat states with identical one-body data can exhibit distinct connected four-point correlations, which we characterize through the four-point Majorana Wick error and, equivalently, the connected two-body reduced density matrix cumulant. We show that this quartic structure is necessarily nonzero and formulate its extremization as a two-body reduced density matrix (2RDM) purity problem. Combining this framework with a Hilbert--Schmidt estimate of Christiansen for truncated two-body correlations, we obtain an upper bound on the connected quartic structure in terms of first antiflatness. Our results establish both a complete characterization of maximal fermionic antiflatness at fixed particle number and a constrained hierarchy linking covariance-level flatness to higher-order non-Gaussian correlations.
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BibTeX
@misc{gupta2026maximally,
title = {{Maximally antiflat fixed-particle-number fermionic states}},
author = {Rahul Gupta and Arya Haghighian and James D. Whitfield},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13903},
eprint = {2610.13903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13903},
}
RIS
TY - UNPB
TI - Maximally antiflat fixed-particle-number fermionic states
AU - Rahul Gupta
AU - Arya Haghighian
AU - James D. Whitfield
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13903
UR - https://arxiv.org/abs/2610.13903
AB - Fermionic Gaussian states are completely characterized by their two-point correlations, making the covariance matrix a natural reference for quantifying non-Gaussian structure. Motivated by fermionic antiflatness, we study its extremal form for pure number-conserving states and ask which states can be maximally antiflat and how they can be constructed. We show that, at fixed particle number, maximal first antiflatness is equivalent to a completely flat one-body reduced density matrix, and we obtain a complete existence classification together with explicit block and cyclic-orbit constructions of all allowed sectors. We then investigate the structure that appears beyond the covariance level. Maximally antiflat states with identical one-body data can exhibit distinct connected four-point correlations, which we characterize through the four-point Majorana Wick error and, equivalently, the connected two-body reduced density matrix cumulant. We show that this quartic structure is necessarily nonzero and formulate its extremization as a two-body reduced density matrix (2RDM) purity problem. Combining this framework with a Hilbert--Schmidt estimate of Christiansen for truncated two-body correlations, we obtain an upper bound on the connected quartic structure in terms of first antiflatness. Our results establish both a complete characterization of maximal fermionic antiflatness at fixed particle number and a constrained hierarchy linking covariance-level flatness to higher-order non-Gaussian correlations.
ER -