Von Neumann entropy and majorization

Abstract

We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel $\Phi$, one has $S(\Phi (\rho ))=S(\rho )$ for all quantum states $\rho$ if and only if there exists an isometric operator $V$ such that $\Phi (\rho )=V\rho V^{\ast }$.

Version 2 contains some corrections and linguistic improvements

References in corpus (1)

• Diagonals of self-adjoint operators

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