The classical-quantum boundary for correlations: Discord and related measures

Modi, Kavan; Brodutch, Aharon; Cable, Hugo; Paterek, Tomasz; Vedral, Vlatko

doi:10.1103/revmodphys.84.1655

Cited by 1,578 publications

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References 353 publications

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“…Now we consider the case of bipartite state ρ AB in tensor space H A ⊗ H B [8]. Recall that quantum discord is a kind of quantum correlation that is different from the entanglement and has found many novel applications [9]. A bipartite state ρ AB is of zero discord if and only if it is a classical-quantum correlated state (CQ state).…”

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confidence: 99%

Uncertainty relations based on skew information with quantum memory

Ma¹,

Chen²,

Fei³

2016

Sci. China Phys. Mech. Astron.

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PACS number(s): 03.67. 75.10.Pq, 03.67.Mn Dear Editors, Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be simultaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum mechanics and has been investigated in terms of various types of uncertainty inequalities: as informational recourses in entropic terms, by means of majorization technique and based on sum of variances and standard deviations.For a pair of observables R and S , the well-known Heisenberg-Robertson uncertainty relation [1] says that,, where [R, S ] = RS − S R is the commutator and V ρ (R) is the standard deviation of R. The entropies serve as appropriate measures of the information content. It is also used to quantify the quantum uncertainty: the sum of the Shannon entropy of the probability distribution of the outcomes is no less than log 2 1 c [2] when R and S are measured. The term 1/c quantifies the complementarity of the two observables R and S . It has been proved that the entropy uncertainty relations do imply the Heisenberg's uncertainty relation.Concerning bipartite systems, the authors in [3] provided a bound on the uncertainties which depends on the amount of entanglement between the measured particle A and the quantum memory B. The result of [3] was further improved to depend on the quantum discord between particles A and B in [4]. Recently the authors in [5] obtained entropic uncertainty relations for multiple measurements with quantum memory.The quantum uncertainty relation can be also described in terms of skew information. I (ρ, H) = − 1 2 Tr √ ρ, H 2 is introduced to quantify the degree of non-commutativity of a state ρ and an observable H, which is reduced to the variance V ρ (H) when ρ is a pure state [6]. It can be interpreted as quantum uncertainty of H in ρ. Luo introduced another quantity, where {X, Y} is the anticommutator, H 0 = H − Tr(ρH)I with I the identity operator. The following inequality holds [7],I (ρ, R) J ρ (R) can be regarded as a kind of measure for quantum uncertainty.Hence we define UN(ρ, R) := I (ρ, R) J ρ (R). Then we define the uncertainty of ρ associated to the projective measurement {φ k } as:, where φ k = |φ k φ k | and ψ k = |ψ k ψ k | are the rank one spectral projectors of two non-degenerate observables R and S with eigenvectors |φ k and |ψ k , respectively. Now we consider the case of bipartite state ρ AB in tensor space H A ⊗ H B [8]. Recall that quantum discord is a kind of quantum correlation that is different from the entanglement and has found many novel applications [9]. A bipartite state ρ AB is of zero discord if and only if it is a classical-quantum correlated state (CQ state). Besides the definition of the original discord, there are some other discord-like measures sharing the same properties such that their values are zero iff the state is a CQ sta...

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confidence: 99%

Uncertainty relations based on skew information with quantum memory

Ma¹,

Chen²,

Fei³

2016

Sci. China Phys. Mech. Astron.

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“…However, it is not the only kind of quantum correlation useful for quantum information processing [5][6][7][8][9]. It has been pointed out that some tasks can be sped up over their classical counterparts using fully separable and highly mixed states, i.e., states with no entanglement but have nonzero quantum discord [10][11][12][13][14][15][16]. Quantum discord is another kind of quantum correlation di erent from entanglement.…”

Section: Introductionmentioning

confidence: 99%

Effects of phase shift on bipartite and multipartite correlations of a spin chain under dephasing

Chen

Zhang

2015

Open Physics

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Abstract:We investigate the e ects of phase shift on entanglement, quantum discord, geometric discord, and spinsqueezing of a Heisenberg chain under dephasing. An analytical solution of the present model is obtained. Our results show that the initial correlations of the spin chain could be partially stored for a long time in the presence of dephasing and the amount of steady state correlations can be adjusted via phase shift. Particularly, we nd the e ects of phase shift on quantum discord and geometric discord are not always the same, i.e., the increase of geometric discord does not always imply the increase of quantum discord. Then, we calculate the spin-squeezing of the spin chain and nd that spin-squeezing rst increases with time and then reaches a plateau. The amount of spin-squeezing can be controlled via phase shift.

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“…Various notions of quantumness of correlations exist in the literature (see, for example, [1,2]). We restrict our attention to the simplest non-trivial case of two-partite systemtwo-qubit system.…”

Section: Introductionmentioning

confidence: 99%

Classification of two-qubit states

Caban

Rembieliński

Smoliński

et al. 2015

Quantum Inf Process

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Verstraete, Dehaene and DeMoor showed that each of the two-qubit states can be generated from one of two canonical families of two-qubit states by means of transformations preserving the tensor structure of the state space. Precisely, each of such states can be generated from a three-parameter family of Bell-diagonal states or from three-parameter rank-deficient states. In this paper, we show that this classification of two-qubit states can be refined. In particular, we show that the latter canonical family of states can be reduced to three fixed states and a two-parameter family of two-qubit states. For this family of states, we provide a simple parametrization that guarantees positive semidefiniteness of the states and enables easier calculation of the Wootters concurrence and quantum discord. Moreover, we present a new general parametrization of all two-qubit states generated from the canonical families of states using sets of (pseudo)orthogonal four-vectors (frames). An advantage of the presented approach lies in the fact that the standard conditions for positive semidefiniteness of states are equivalent to (pseudo)orthogonality conditions for four-vectors serving as This work has been supported by the Polish National Science Centre under the contract 2014/15/B/ST2/00117 and by the University of Lodz.

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The classical-quantum boundary for correlations: Discord and related measures

Cited by 1,578 publications

References 353 publications

Uncertainty relations based on skew information with quantum memory

Uncertainty relations based on skew information with quantum memory

Effects of phase shift on bipartite and multipartite correlations of a spin chain under dephasing

Classification of two-qubit states

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