Structural Characterization And Condition For Measurement Statistics Preservation Of A Unital Quantum Operation

TL;DR

This paper characterizes the fixed points of unital quantum operations on finite-dimensional states, providing conditions for measurement statistics preservation and extending previous results on quantum channel capacities.

Contribution

It offers a complete characterization of states fixed by unital quantum operations and clarifies conditions for measurement statistics preservation, extending prior theoretical work.

Findings

Complete characterization of fixed states by unital quantum operations

Necessary and sufficient conditions for measurement statistics preservation

Extension of capacity and entropy reduction theorems for unital channels

Abstract

We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation $\phi$ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with $\phi$, we can completely characterize the kind of quantum states that are fixed by $\phi$. Our work has several applications. It gives a simple proof of the structural characterization of a unital quantum operation that acts on finite-dimensional quantum states --- a result not explicitly mentioned in earlier studies. It also provides a necessary and sufficient condition for what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of St{\o}rmer by giving a proof of a reduction theorem on the unassisted and entanglement-assisted classical capacities, coherent information, and minimal output Renyi entropy of a unital channel acting on finite-dimensional quantum state.