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The red solid line, black solid line and blue solid line represent the quantum correlation entropy of ε(ρ2), ε(ρ3), and ε(ρ4), respectively. The noisy channel is bit-phase flip channel. We take c2 = 0.8, c1 = 0.5, and c3 = c2 ⋅ c1. The red dotted line represents the value of − f(c2). The red diamond is the intersection of quantum correlation entropy of ε(ρ3) and ε(ρ4). The green diamond is the intersection of quantum correlation entropy of ε(ρ2) and ε(ρ4). The yellow diamond is the intersection of quantum correlation entropy of ε(ρ2) and ε(ρ3). Let the horizontal coordinates of the red diamond, green diamond and yellow diamond be R◇, G◇ and Y◇, respectively
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Quantum correlation entropy is used to measure total non-classical correlation of multiple states. It is based on a local coarse-grained measurement. Quantum noisy processes have a theoretically and experimentally important role in quantum information tasks. We study the dynamical behavior of quantum correlation entropy of output state under the ef...
Citations
... The observational entropy [63][64][65][66][67] and measured relative entropy [68][69][70] have been topics of recent interest in physical [63][64][65][66][67][71][72][73][74][75][76][77][78][79][80][81][82][83] and information theoretic [84][85][86][87][88][89][90] applications, due to the role of observational entropy connecting coarse-graining to statistical mechanics [63][64][65][66][67][91][92][93][94]. The quantity D M (ρ∥σ) describes how well a measurement M can distinguish between ρ, σ. ...
We investigate four partial orderings on the space of quantum measurements (i.e. on POVMs or positive operator valued measures), describing four notions of coarse/fine-ness of measurement. These are the partial orderings induced by: (1) classical post-processing, (2) measured relative entropy, (3) observational entropy, and (4) linear relation of POVMs. The orderings form a hierarchy of implication, where e.g. post-processing relation implies all the others. We show that this hierarchy is strict for general POVMs, with examples showing that all four orderings are strictly inequivalent. Restricted to projective measurements, all are equivalent. Finally we show that observational entropy equality SM = SN (for all ρ) holds if and only if POVMs M ≡ N are post-processing equivalent, which shows that the first three orderings induce identical equivalence classes.
... B Qiong Guo with the original one for bipartite systems. Subsequently, more research works on multipartite quantum discord were conducted [15][16][17][18][19]. ...
In this paper, we investigate the quantum discord for a family of three-qubit extended X-states and give analytic formulas of the quantum discord for three-qubit states in several cases, including two zero quantum discord cases and the Werner-GHZ state case. Moreover, we inspect the dynamic behavior of the quantum discord for the three-qubit states under the phase damping channel. It is shown that the frozen phenomenon of quantum discord exists for some states under phase damping channel, while it does not exist for some other states. In particular, the quantum discord of the Werner-GHZ state monotonically decreases to zero under the phase damping channel.
... [1][2][3][4] in studies of non-equilibrium statistical mechanics as a useful unifying framework to describe coarse-grained entropy in classical and quantum systems, [5][6][7] with applications across thermodynamics and quantum information theory. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] In the quantum case, for any measurement described by a positive operator valued measures (POVM) M = (Mi)i ∈ I , (Mi ≥ 0, ∑ i Mi = ), and quantum state described by a density matrix ρ, observational entropy ...
... The existence of such states was demonstrated in Lemma 4. From (26) we have two different convex decompositions ω = λ ω 1 + (1 − λ)ω 2 , both with the same coefficients λ = 1/(1 + ϵ). By the assumption (18) of bounded concavity, ...
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general positive operator valued measures measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound.
... Quantum correlation entropy is such a measure [9]. Observational entropy has applications in quantum statistical thermodynamics [10,11] and quantum correlation theory [12,13]. ...
A superposition measure with respect to coarse-grained measurement is presented in this paper. We consider a special kind of mixed states—the generalized n-qubit Werner state as the initial state. We take an appropriate coarse-graining acting on the initial state and find that the observational entropy and the von Neumann entropy are equal for any n. Furthermore, for another coarse-graining, we study the difference between observational entropy and von Neumann entropy. We find that this difference satisfies the condition of superposition measure, so this difference can be regarded as a superposition measure with respect to a coarse-grained measurement. The characterizations of this superposition measure are studied.
... Observational entropy has recently emerged (in fact, re-emerged, cf. [1][2][3][4]) in studies of nonequilibrium statistical mechanics as a useful unifying framework to describe coarse-grained entropy in classical and quantum systems [5][6][7], with applications across thermodynamics and quantum information theory [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. ...
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex a set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound.
