# zbMATH — the first resource for mathematics

Transformations on density operators that leave the Holevo bound invariant. (English) Zbl 1302.81048
Summary: For a given probability distribution $$\lambda_1,\dots,\lambda_m$$ we determine the structure of all such maps defined on a dense subset of density operators which leave the Holevo bound invariant i.e. which satisfy $S\left(\sum\limits_{k=1}^m \lambda_k \phi(\rho_k)\right)-\sum\limits_{k=1}^m \lambda_k S\left(\phi (\rho_k)\right)= S\left(\sum\limits_{k=1}^m \lambda_k \rho_k\right)-\sum_{k=1}^m \lambda_k S(\rho_k)$ for all possible collections $$\rho_1,\dots,\rho_m$$ of density operators.

##### MSC:
 81P15 Quantum measurement theory, state operations, state preparations 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
Full Text:
##### References:
 [1] Briët, J.; Harremoës, P., Properties of classical and quantum Jensen-Shannon divergence, Phys. Rev. A, 79, (2009) [2] Klauck, H.; Nayak, A.; Ta-Shma, A.; Zuckerman, D., Interaction in quantum communication, IEEE Trans. Inf. Theory, 53, 1970-1982, (2007) · Zbl 1323.94066 [3] Molnár, L.: Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces. Lecture Notes in Mathematics, vol. 1895. Springer, Berlin (2007) · Zbl 1119.47001 [4] Molnár, L.; Timmermann, W., Maps on quantum states preserving the Jensen-Shannon divergence, J. Phys. A, Math. Theor., 42, (2009) · Zbl 1156.81349 [5] Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) · Zbl 1049.81015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.