General monogamy property of global quantum discord and the application

Liu, Siyuan; Zhang, Yu-Ran; Li-ming, Zhao; Yang, Wen-Li; Fan, Heng

doi:10.1016/j.aop.2014.05.015

Cited by 34 publications

(15 citation statements)

References 52 publications

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“…In recent years, the relation between QPTs and quantum information has caused great attention, and several concepts borrowed from quantum information science are successfully used in the study on QPTs 6 7 8 9 10 11 12 13 14 15 ; these concepts include entanglement 8 9 , mutual information 10 , quantum fidelity 12 14 , and quantum discord (QD) 15 16 17 . Very recently, the relationship between QPTs and the ground-state local convertibility is investigated in ref.…”

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confidence: 99%

Quantum coherence and quantum phase transitions

Lin

2016

Sci Rep

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We study the connections between local quantum coherence (LQC) based on Wigner-Yanase skew information and quantum phase transitions (QPTs). When applied on the one-dimensional Hubbard, XY spin chain with three-spin interaction, and Su-Schrieffer-Heeger models, the LQC and its derivatives are used successfully to detect different types of QPTs in these spin and fermionic systems. Furthermore, the LQC is effective as the quantum discord (QD) in detecting QPTs at finite temperatures, where the entanglement has lost its effectiveness. We also demonstrate that the LQC can exhibit different behaviors in many forms compared with the QD.

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confidence: 99%

Quantum coherence and quantum phase transitions

Lin

2016

Sci Rep

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“…Thus, all classical extensions of separable states are polygamous in the usual sense. This observation i) constitutes the basic argument in demonstrating that quantum correlations are not monogamous in general [25] and ii) underlies the violation of more general monogamy relations, even for multipartite correlation measures [29,30]. However, there exist monogamy relations valid even for classical extensions if we consider some generalized multipartite quantum correlations.…”

Section: Monogamy Of Correlationsmentioning

confidence: 99%

Quantum state space dimension as a quantum resource

Plastino

Bellomo

Plastino

2015

Int. J. Quantum Inform.

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We argue that the dimensionality of the space of quantum systems' states should be considered as a legitimate resource for quantum information tasks. The assertion is supported by the fact that quantum states with discord-like capacities can be obtained from classically correlated states in spaces of dimension large enough. We illustrate things with some simple examples that justify our claim.Keywords: Hilbert space, quantum information, quantum discordThe Hilbert-space dimension has been related to physical resources for different physical systems, playing a fundamental role in quantum computation. Basically, the idea is that "if you want to avoid supplying an amount of some physical resource that grows exponentially with problem's size, the computer must be made up of parts whose number grows nearly linearly with the number of qubits required in an equivalent quantum computer. This thus becomes a fundamental requirement for a system to be a scalable quantum computer" [1]. Moreover, some recent results show that quantum dimensionality could be regarded as a physical entity. For example, Brunner et al. defined what they call 'dimension witnesses': observable quantities to estimate the minimum dimension of a given system state-space consistent with a number of measured correlations [2][3][4]. In the same spirit, Wehner et al. found a lower bound that gives a fundamental limit on the dimension of the state to implement certain measurement strategies [5]. Here, we propose to consider the dimension of the Hilbert space as a legitimate resource for quantum information processing. Our main argument lies in the observation, due to Li and Luo [6], that quantum separable states can be obtained from reductions of classically correlated ones. Although some authors have suggested the possibility of understanding the size of the Hilbert space as a resource by itself [7], the assertion that it is a quantum-better-than-classical resource was never technically analyzed, as far as we know.Under the discord paradigm, a classically correlated state (or simply, a classical state) is one that is information-wise accessible to local observers. Given a discord-like measure δ and a classical state σ AB of a composite system A + B, one knows that δ(σ AB ) = 0. The following theorem, due to Li and Luo, demonstrates a notable relation between separable states and classical states [6]. Figure 1. Every quantum state that is separable (within a given bipartition of the full system) is, in a formal sense, the reduction of a classical state of a system defined over a larger state-space (and preserves the original bipartition). Here, the state σ AB of the composite A + B should be regarded as a classical extension of the separable ρ ab .The proof is given by Li and Luo in Ref. [6]. The next result follows directly from the above theorem: Proposition. Any quantum task carried out using unentangled states can also be undertaken using classically correlated states.Indeed, if a quantum task needs appealing to a given un-entangled state ρ ab , then ...

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“…It is well known that classical correlations are infinitely shareable whereas there is a restriction on the shareability of quantum entanglement amongst the several parts of a multipartite quantum state [1][2][3][4]. The concept of monogamy of entanglement and monogamy of quantum correlations has been studied quite extensively [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and it is shown that the measures of quantum correlations such as quantum discord [19], quantum deficit [20] are not monogamous for some category of pure states [11,12]. The polygamous nature of quantum correlations other than entanglement has initiated discussions on the properties to be satisfied by a correlation measure to be monogamous [16] and it is shown that a measure of correlations is in general non-monogamous if it does not vanish on the set of all separable states [16].…”

Section: Introductionmentioning

confidence: 99%

What Does Monogamy in Higher Powers of a Correlation Measure Mean?

Geetha¹,

nbsp²,

Sudha³

et al. 2014

JMP

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We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality need not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.

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General monogamy property of global quantum discord and the application

Cited by 34 publications

References 52 publications

Quantum coherence and quantum phase transitions

Quantum coherence and quantum phase transitions

Quantum state space dimension as a quantum resource

What Does Monogamy in Higher Powers of a Correlation Measure Mean?

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