Quantum versus Classical Correlations in Gaussian States

Adesso, Gerardo; Datta, Animesh

doi:10.1103/physrevlett.105.030501

Cited by 483 publications

(640 citation statements)

References 31 publications

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“…Quantum discord was analytically computed for a class of 2-qubit state [17,18]. Finally, it was recently generalized for systems with continuous variables to study the correlations in Gaussian states [19,20]. Interestingly, it was shown [21] that a set of states with vanishing discord has vanishing volume in the set of all states.…”

Section: Introductionmentioning

confidence: 99%

Witnessing quantum discord in2×Nsystems

2010

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Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show 2 × N states satisfy additional property: the positivity of their partial transposition is recognized with respect to the canonical factorization of the original density operator. We call such states SPPT (for strong PPT). Therefore, we provide a natural witness for a quantum discord: if a 2 × N state is not SPPT it must contain nonclassical correlations measured by quantum discord. It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.

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Section: Introductionmentioning

confidence: 99%

Witnessing quantum discord in2×Nsystems

2010

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“…enumerate components of fourvectors. Furthermore, under the transformation (14) e α σ → e α σ = A(ẽ α σ )A † , e α = Λ(A)ẽ α (19) and transformed four-vectors {e α } form a frame, too:…”

Section: Two-qubit Statesmentioning

confidence: 99%

“…Since evaluation of quantum discord involves a complicated optimization procedure, the analytical expressions for quantum discord are known only for two-qubit Bell-diagonal states [10], for seven-parameter two-qubit X states [11] (not always correct exactly, but approximately correct with a very small absolute error [12]), for two-mode Gaussian states [13,14], for a class of two-qubit states with parallel nonzero Bloch vectors [15] and for two-qubit Werner and isotropic states [16]. Despite this fact, quantum discord has been studied in different contexts [2].…”

Section: The Orbit Generated By the State σ IV [Eq (12)]mentioning

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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“…Now, it is well understood that almost all quantum states, including unentangled (separable) ones, possess quantum correlations. However, the analytical evaluation of quantum discord requires extremization procedures that can be tedious to achieve [27,28,29,30,31,32,33,34]. To overcome this difficulty, a geometrical approach was proposed in [35].…”

Section: Introductionmentioning

confidence: 99%

Unified scheme for correlations using linear relative entropy

Daoud

Laamara²,

Kaydi³

2014

Physics Letters A

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A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which we determine the total, classical and quantum correlations. We also give the explicit expressions of its closest product state, closest classical state and the corresponding closest product state. A closed additive relation, involving the various correlations quantified by linear relative entropy, is derived.

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Quantum versus Classical Correlations in Gaussian States

Cited by 483 publications

References 31 publications

Witnessing quantum discord in2×Nsystems

Witnessing quantum discord in2×Nsystems

Classification of two-qubit states

Unified scheme for correlations using linear relative entropy

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