Von Neumann Entropy-Preserving Quantum Operations

Abstract

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

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