Entropy-energy inequalities for qudit states

Abstract

We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of restricting the extremal density matrices by pure states, we show that the energy spectra of the Hamiltonian is recovered for $d=2$ and $3$. We conjecture that by means of this approach the energy spectra can be recovered for the Hamiltonian of an arbitrary finite qudit system. For a given qudit system Hamiltonian, we find new inequalities connecting the mean value of the Hamiltonian and the entropy of an arbitrary state. We demonstrate that these inequalities take place for both the considered extremal density matrices and generic ones.

arXiv comment12 pages, 4 figures Accepted for publication in Journal of Physics A: Mathematical and Theoretical

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Cited by in corpus (5)

• New entropic inequalities for qubit and unimodal Gaussian states
• Entropic bounds between two thermal equilibrium states
• Minkovskii-type inequality for arbitrary density matrix of composite and noncomposite systems
• Hidden correlations in indivisible qudits as a resource for quantum technologies on examples of superconducting circuits
• Entanglement of extremal density matrices of 2-qubit Hamiltonian with Kramers degeneracy