Related papers: Optimal Hamiltonian for a quantum state with finite entropy

Optimal Hamiltonian for a quantum state with finite entropy

URL: http://arxiv.org/abs/2508.16575v1
Date: Fri, 22 Aug 2025 17:58:26 GMT
Title: Optimal Hamiltonian for a quantum state with finite entropy
Authors: M. E. Shirokov,
Abstract summary: We show that for any mixed state $rho$ with finite entropy and any $E>0$ there is a unique solution $H(rho,E_0,E)$ of the problem.<n>Explicit expressions for $H(rho,E_0,E)$ and $S(gamma_H(E))$ with $H=H(rho,E_0,E)$ are obtained.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We consider the following task: how for a given quantum state $\rho$ to find a grounded Hamiltonian $H$ such that $\mathrm{Tr}H\rho\leq E_0<+\infty$ in such a way that the von Neumann entropy of the Gibbs state $\gamma_H(E)$ corresponding to a given energy $E>0$ be as small as possible. We show that for any mixed state $\rho$ with finite entropy and any $E>0$ there is a unique solution $H(\rho,E_0,E)$ of the above problem which we call optimal Hamiltonian for this state. Explicit expressions for $H(\rho,E_0,E)$ and $S(\gamma_H(E))$ with $H=H(\rho,E_0,E)$ are obtained. Several examples are considered. A brief overview of possible applications is given (with the intention to give a detailed description in a separate article).

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