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Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
, 2014
"... This paper defines the fidelity of recovery of a tripartite quantum state on systems A, B, and C as a measure of how well one can recover the full state on all three systems if system A is lost and a recovery operation is performed on system C alone. The surprisal of the fidelity of recovery (its ne ..."
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Cited by 4 (1 self)
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This paper defines the fidelity of recovery of a tripartite quantum state on systems A, B, and C as a measure of how well one can recover the full state on all three systems if system A is lost and a recovery operation is performed on system C alone. The surprisal of the fidelity of recovery (its negative logarithm) is an information quantity which obeys nearly all of the properties of the conditional quantum mutual information I(A;BC), including nonnegativity, monotonicity under local operations, duality, and a dimension bound. We then define an entanglement measure based on this quantity, which we call the geometric squashed entanglement. We prove that the geometric squashed entanglement is an entanglement monotone, that it vanishes if and only if the state on which it is evaluated is unentangled, and that it reduces to the geometric measure of entanglement if the state is pure. We also show that it is subadditive, continuous, and normalized on maximally entangled states. We next define the surprisal of measurement recoverability, which is an information quantity in the spirit of quantum discord, characterizing how well one can recover a share of a bipartite state if it is measured. We prove that this discordlike quantity satisfies several properties, including nonnegativity, faithfulness on classicalquantum states, invariance under local isometries, dimension bounds, and normalization on maximally entangled states. This quantity combined with a recent breakthrough of Fawzi and Renner allows to characterize states with discord nearly equal to zero as being approximate fixed points of entanglement breaking channels (equivalently, they are recoverable from the state of a measuring apparatus). Finally, we discuss a multipartite fidelity of recovery and several of its properties.
Strong converse exponents for a quantum channel discrimination problem and quantumfeedbackassisted communication.
, 2014
"... Summary: We study the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. Background: Quantum channel discrimination is a natural extension of a basic problem in quantum hypothesis testing, ..."
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Summary: We study the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. Background: Quantum channel discrimination is a natural extension of a basic problem in quantum hypothesis testing, that of distinguishing between the possible states of a quantum system. In an i.i.d. binary state discrimination problem, the discriminator is provided with n quantum systems in the state ρ ⊗n or σ ⊗n , and the task is to apply a binary measurement {Q n , I ⊗n − Q n } to these n systems, with 0 ≤ Q n ≤ I ⊗n . One is then concerned with two kinds of error probabilities: α n (Q n ) ≡ Tr {(I ⊗n − Q n )ρ ⊗n } , the probability of incorrectly rejecting the null hypothesis, the Type I error, and β n (Q n ) ≡ Tr {Q n σ ⊗n } , the probability of incorrectly rejecting the alternative hypothesis, the Type II error. One studies the asymptotic behaviour of α n and β n as n → ∞, expecting there to be a tradeoff between minimising α n and minimising β n . In quantum channel discrimination, we have a quantum channel with input system A and output system B, and we are given that the channel is described by either the completely positive trace1 A more detailed version of this work is available on the arXiv,
Strong converse for the quantum capacity of the erasure channel for almost all codes
 the Proceedings of the 9th Conference on the Theory of Quantum Computation, Communication and Cryptography
, 2014
"... channel for almost all codes ..."
Rényi generalizations of quantum information measures
"... Summary. Our main result is a procedure to obtain a Rényi generalization of any quantum information measure which consists of (a) a linear combination of von Neumann entropies with coefficients chosen from the set {−1, 0, 1} [2], or, (b) a difference of two relative entropies A quantum Rényi condi ..."
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Summary. Our main result is a procedure to obtain a Rényi generalization of any quantum information measure which consists of (a) a linear combination of von Neumann entropies with coefficients chosen from the set {−1, 0, 1} [2], or, (b) a difference of two relative entropies A quantum Rényi conditional entropy and mutual information have been proposed and studied