Abstract
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation ϕ acting on finite-dimensional quantum states. By reducing this problem to the problem of simultaneous diagonalization of the Kraus operators associated with ϕ, we can completely characterize the kinds of quantum states that are fixed by ϕ. 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 determining what kind of measurement statistics is preserved by a unital quantum operation. Finally, our result clarifies and extends the work of Størmer 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 a finite-dimensional quantum state.
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