C. King, A. Lesniewski, Quantum Sources and a Quantum Coding Theorem, J. Math. Phys. 39 (1), 88-101 (1998) Home/Search Document Not in Database Summary Related Articles Check |
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The Shannon-McMillan Theorem for Ergodic Quantum.. - Bjelakovic, Krüger.. (Correct)
....to establish a quantum version of the Shannon McMillan theorem for stationary quantum systems. Due to the fact that in quantum theory there exist several entropy notions (cf. 1] depending on e.g. how the measuring process is incorporated, there is a number of different approaches. The paper [13] of King and Lesniewski concerns the classical stochastic process obtained from an ergodic quantum source by measurements of the individual components and derives an asymptotic dimension of a relevant subspace in terms of the classical mean entropy. This relevant subspace however is in general not ....
C. King, A. Lesniewski, Quantum Sources and a Quantum Coding Theorem, J. Math. Phys. 39 (1), 88-101 (1998)
Quantum Information Theory - Barnum, III (1998) (Correct)
....satisfy the (classical) AEP; however, these are not necessarily all the sources which satisfy it. There is as yet no known quantum analogue to the Shannon McMillan Breiman theorem, providing a broad and natural class of sources satisfying the QAEP, although there has been work in this direction [42]. King and Lesniewski have found some interesting results which apply to quantum sources. They use the entropy hA of a classical source generated by measuring a complete set A of orthogonal projectors on each copy of the source Hilbert space, i.e. by measuring A Omega n on H Omega n , to ....
C. King and A. Lesniewski, "Quantum sources and a quantum coding theorem," Journal of Mathematical Physics, vol. 39, pp. 88--101, 1998.
On Quantum Fidelities and Channel Capacities - Barnum, Knill, Nielsen (2000) (5 citations) (Correct)
....satisfy the (classical) AEP; however, these are not necessarily all the sources which satisfy it. There is as yet no known quantum analogue of the Shannon McMillan Breiman theorem, providing a broad and natural class of sources satisfying the QAEP, although there has been work in this direction [31]. SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 4 III. Useful facts about fidelities A. Convexity of Entanglement Fidelity in the Input Density Operator Lemma 1: The entanglement delity is convex in the input density operator, F e ( 1 (1 ) 2 ) E) F e ( 1 ; E) 1 )F e ( 2 ....
C. King and A. Lesniewski, \Quantum sources and a quantum coding theorem," J. Math. Phys., vol. 39, pp. 88-101, 1998.
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