Download Communications in Mathematical Physics - Volume 266 by M. Aizenman (Chief Editor) PDF

By M. Aizenman (Chief Editor)

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2 q ≥ p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 39 39 40 42 43 43 44 46 47 48 49 50 50 52 38 I. Devetak, M. Junge, C. B. Ruskai 5. Applications of CB Entropy . . . . . 1 Examples and bounds . . . . . 3 Operational interpretation . . . . 6. Entropy Inequalities . . . .

Since Rk is a density matrix, Tr2 (Rk ) p ≤ 1. 3. Operational interpretation. Recently Horodecki, Oppenheim and Winter [18, 19] (HOW) obtained results which give an important operational meaning to quantum conditional information, consistent with both positive or negative values. 1) gives the following interpretation: Multiplicativity of Completely Bounded p-Norms Implies New Additivity Result 57 • A channel for which SCB,min ( ) > 0 always breaks enough entanglement so that some EPR pairs must be added to enable Alice to transfer her information to Bob.

38 39 39 40 42 43 43 44 46 47 48 49 50 50 52 38 I. Devetak, M. Junge, C. B. Ruskai 5. Applications of CB Entropy . . . . . 1 Examples and bounds . . . . . 3 Operational interpretation . . . . 6. Entropy Inequalities . . . . . . . A. Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 53 55 56 57 61 1. Introduction Quantum channels are represented by completely positive, trace preserving (CPT) maps on Md , the space of d × d matrices.

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