On Entangled Information and Quantum Capacity
Tóm tắt
The pure quantum entanglement is generalized to the case of mixed compound states to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized as transpose-CP but not CP maps. The entangled information is introduced as the relative entropy of the mutual and the input state and total information of the entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the supremum of the information over all c-entanglements, and the true quantum entropy, which is achieved at the standard entanglement. The q-capacity, defined as the supremum over all entanglements, doubles the c-capacity in the case of the simple algebra. The conditional q-entropy is positive, and q-information of a quantum channel is additive.
Tài liệu tham khảo
V. P. Belavkin, Open Sys. Information Dyn. 7, 101 (2000).
C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
B. Schumacher, Phys. Rev. A 51, 2614 (1993); Phys. Rev. A 51, 2738 (1993); Phys. Rev. A 54, 2614 (1996).
R. Jozsa and B. Schumacher, J. Mod. Opt. 41, 2343 (1994).
V. P. Belavkin and M. Ohya, Los Alamos Archive: quant-ph/9812082.
V. P. Belavkin and M. Ohya, Los Alamos Archive: quant-ph/0004069.
G. Lindblad, Comm. Math. Phys. 33, 305 (1973).
H. Araki, “Relative Entropy of states of von Neumann Algebras”, in: Publications RIMS, Kyoto University, 11, 809 (1976).
H. Umegaki, Kodai Math. Sem. Rep. 14, 59 (1962).
V. P. Belavkin and P. Staszewski, Annals de l'institut Henri Poincare: Phys. Theor. 37, 51 (1982).
V. P. Belavkin and P. Staszewski, Rep. Math. Phys. 20, 373 (1984).
V. P. Belavkin and P. Staszewski, Rep. Math. Phys. 24, 24 (1986).
M. Ohya and D. Petz, Quantum Entropy and Its Use, Springer, 1993.
W. F. Stinespring, Proc. Amer. Math. Soc. 6, 211 (1955).
K. Kraus, Ann. Phys. 64, 311 (1971).
A. Uhlmann, Commun. Math. Phys. 54, 21 (1977).
A. S. Holevo, Probl. Peredachi Inform. 9, no. 3, 3 (1973).
R. S. Stratonovich and A. G. Vancian, Probl. Control Inform. Theory 7, no. 3, 161 (1978).
P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, W. Wootters, Phys. Rev. A 54, 1869 (1996).