Semicontinuity bounds for the von Neumann entropy and partial majorization

• URL: http://arxiv.org/abs/2504.08098v1
• Date: Thu, 10 Apr 2025 19:55:06 GMT
• Title: Semicontinuity bounds for the von Neumann entropy and partial majorization
• Authors: M. E. Shirokov,
• Abstract summary: We consider families of tight upper bounds on the difference $S(rho)-S(sigma)$ with the rank/energy constraint imposed on the state $rho$.<n>The upper bounds within these families depend on the parameter $m$ of partial majorization.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider families of tight upper bounds on the difference $S(\rho)-S(\sigma)$ with the rank/energy constraint imposed on the state $\rho$ which are valid provided that the state $\rho$ partially majorizes the state $\sigma$ and is close to the state $\sigma$ w.r.t. the trace norm. The upper bounds within these families depend on the parameter $m$ of partial majorization. The upper bounds corresponding to $m=1$ coincide with the optimal semicontinuity bounds for the von Neumann entropy with the rank/energy constraint obtained in [Lett.Math.Phys.,113,121,35] and [arXiv:2410.02686]. We also consider classical versions of the above results formulated in terms of probability distributions and the Shannon entropy.

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