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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

One-parameter counterexamples to the refined Bessis-Moussa-Villani conjecture

arXiv
Authors: Hyunho Cha

Year

2026

Paper ID

35960

Status

Preprint

Abstract Read

~2 min

Abstract Words

115

Citations

N/A

Abstract

The Bessis-Moussa-Villani (BMV) conjecture, originating in quantum statistical mechanics, was proved by Stahl after an influential reformulation by Lieb and Seiringer. A later refinement asks whether the normalized average over all words with n letters A and m letters B is always bounded above by tr\(AnBm\) and below by trexp\(nlog A+mlog B\). We study a specific one-parameter family \(Ax, Bx\) and derive exact closed formulas for both sides of the first inequality when n=m=5. In particular, x=10-3 gives a counterexample and, remarkably, the ratio of the normalized word average to the trace tr\(AnBm\) can become arbitrarily large.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • The Bessis-Moussa-Villani (BMV) conjecture, originating in quantum statistical mechanics, was proved by Stahl after an influential reformulation by Lieb and Seiringer.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.19927 [2] arXiv https://arxiv.org/abs/2603.19927 [3] Publisher https://arxiv.org/abs/2603.19927

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