Von Neumann Entropy-Preserving Quantum Operations

Abstract

For a given quantum state $\rho$ and two quantum operations $\Phi$ and $\Psi$, the information encoded in the quantum state $\rho$ is quantified by its von Neumann entropy $\S (\rho )$. By the famous Choi-Jamiołkowski isomorphism, the quantum operation $\Phi$ can be transformed into a bipartite state, the von Neumann entropy ${\S }^{\mathrm{map}}(\Phi )$ of the bipartite state describes the decoherence induced by $\Phi$. In this Letter, we characterize not only the pairs $(\Phi ,\rho )$ which satisfy $\S (\Phi (\rho ))=\S (\rho )$, but also the pairs $(\Phi ,\Psi )$ which satisfy ${\S }^{\mathrm{map}}(\Phi \circ \Psi )={\S }^{\mathrm{map}}(\Psi )$.

7 pages, LaTeX, to appear Phys. Lett. A

References in corpus (3)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quantum f-divergences and error correction
• Composition of quantum states and dynamical subadditivity

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• Delocalized and Dynamical Catalytic Randomness and Information Flow
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• Structural Characterization And Condition For Measurement Statistics Preservation Of A Unital Quantum Operation
• Spectral moments and entropy rigidity of quantum channels: a three-mode photonic witness