Quantum discord of two-qubit rank-2 states

Shi, M.; Yang, Wei; Jiang, Feng-Jian; Du, Jiangfeng

doi:10.1088/1751-8113/44/41/415304

Cited by 63 publications

(76 citation statements)

References 48 publications

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“…The steering ellipsoid formalism [11][12][13][14] gives a faithful representation of two-qubit states analogous to the Bloch vector picture for a single qubit. Any two-qubit state may be represented by an ellipsoid inside the Bloch sphere, but not all ellipsoids inside the Bloch sphere represent a two-qubit state.…”

Section: Introductionmentioning

confidence: 99%

Geometric representation of two-qubit entanglement witnesses

2015

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Any two-qubit state can be represented geometrically by a steering ellipsoid inside the Bloch sphere. We extend this approach to represent any block positive two-qubit operator B. We derive a classification scheme based on the positivity of det B and det B T B ; this shows that any ellipsoid inside the Bloch sphere must represent either a two-qubit state or a two-qubit entanglement witness. We focus on such witnesses and their corresponding ellipsoids, finding that properties such as witness optimality are naturally manifest in this geometric representation.

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Section: Introductionmentioning

confidence: 99%

Geometric representation of two-qubit entanglement witnesses

2015

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“…Quantum discord for a Bell-diagonal state was analytically obtained [10]. Much research has had a focus on finding the quantum discord of the X state [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Shi et. al [16,17] showed that there are some quantum states where 3 element POVM should be used for optimal quantum discord. The optimality for 3 element POVM can be found by a triangle formed by the direction vectors.…”

Section: Introductionmentioning

confidence: 99%

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

et al. 2015

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“…Applying the map Ω Ω Ω to the classical state σ c = 1 2 (|0 0| ⊗ |0 0| + |1 1| ⊗ |1 1|) leads to ρ = 1 2 (|0 0| ⊗ |0 0| + |1 1| ⊗ |+ +|), which has non-zero discord [34], but vanishing entanglement since it is a convex combination of product states. Given that Ω Ω Ω B (ρ) possesses diagonal elements which are independent of the off-diagonal elements of ρ it has zero distinguishing power for any input state.…”

Section: In Other Words If W (θ θ θmentioning

confidence: 99%

Quantifying the Nonclassicality of Operations

2013

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Deep insight can be gained into the nature of nonclassical correlations by studying the quantum operations that create them. Motivated by this we propose a measure of nonclassicality of a quantum operation utilizing the relative entropy to quantify its commutativity with the completely dephasing operation. We show that our measure of nonclassicality is a sum of two independent contributions, the generating power -its ability to produce nonclassical states out of classical ones, and the distinguishing power -its usefulness to a classical observer for distinguishing between classical and nonclassical states. Each of these effects can be exploited individually in quantum protocols. We further show that our measure leads to an interpretation of quantum discord as the difference in superdense coding capacities between a quantum state and the best classical state when both are produced at a source that makes a classical error during transmission.Introduction. Identifying the resources that underlie quantum advantages in quantum communication and information processing is a crucial question of fundamental and technological importance. Generally, quantum entanglement is ascribed this role due to its necessity in a number of tasks exhibiting quantum advantages [1,2]. However, quantum enhancements are possible in certain computations with limited amounts of entanglement or even none at all when the involved quantum state is mixed [3][4][5][6][7]. Universal quantum computation with pure states also appears to be possible with little entanglement [8]. In addition to computational advantages, quantum communication can also exhibit advantages over classical communication in the absence of entanglement [9][10][11].Recently, it has been suggested that correlations beyond quantum entanglement might provide an explanation behind quantum enhancements. One of the most common quantities is the quantum discord [12][13][14][15]. Quantum discord has recently been interpreted as the difference in the performance of the quantum state merging protocol between a state and its locally decohered equivalent [16], and secondly as quantifying the amount of entanglement consumption in the quantum state merging protocol [17]. The role of quantum discord in a more general family of protocols has also been studied [18].An important difference between quantum discord and entanglement is that the latter is non-increasing, on average, under local operations and classical communication. This is the underlying principle of the resource theory of quantum entanglement. On the other hand, local operations can actually increase quantum discord [19][20][21][22]. Discordant states can be created out of classical states by a local channel if and only if the channel changes the local algebraic structure [23], and several authors have studied the evolution of quantum discord under various forms of dynamics [24][25][26][27][28]. However, the principles underlying the creation of nonclassical correlations from quantum operations are still lacking.Here we investiga...

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Quantum discord of two-qubit rank-2 states

Cited by 63 publications

References 48 publications

Geometric representation of two-qubit entanglement witnesses

Geometric representation of two-qubit entanglement witnesses

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Quantifying the Nonclassicality of Operations

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