Structural characterization and condition for measurement statistics preservation of a unital quantum operation

Kai-Yan Lee, Chi-Hang Fred Fung, H F Chau
2013 Journal of Physics A: Mathematical and Theoretical  
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
more » ... 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.
doi:10.1088/1751-8113/46/20/205305 fatcat:jtvxwa25nrhilp7e26i3o44dyu