Quantum Discord in the Ground State of Spin Chains

Sarandy, M. S.; Oliveira, Thiago R. de; Amico, Luigi

doi:10.1142/s0217979213450306

Cited by 47 publications

(45 citation statements)

References 94 publications

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“…A systematic analysis in this sense, which has only recently been considered [7][8][9][10][11][12][13], is thus highly desirable. This is even more important given that some of the investigations performed so far have indicated that quantum discord is more sensible than entanglement in revealing quantum critical points [9], even for systems that are not at zero temperature [14]. This is a particularly relevant result, whose validity should also be checked for models that are both finite sized and at finite temperature.…”

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confidence: 95%

Global quantum correlations in finite-size spin chains

et al. 2013

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We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.Entanglement and criticality in quantum many-body systems have been shown to be strongly and intimately connected concepts [1,2]. The body of work performed with the aim of grasping the implications that critical changes in the ground state of a given Hamiltonian model have for the sharing of entanglement by the parties of a quantum many-body systems is now quite substantial [3]. This has resulted in important progress in our understanding of the interplay between critical phenomena of interacting many-body systems and the setting up of genuinely quantum features. In turn, such success has proven the effectiveness of the cross-fertilization of quantum statistical mechanics by techniques and interpretations that are typical of quantum information theory.Yet, it has recently emerged that the way correlations of non-classical nature manifest themselves is not necessarily coincident with entanglement, and a much broader definition of quantum correlations should be given [4,5]. This is encompassed very effectively in the formulation of so-called quantum discord as a measure striving to capture the above-mentioned broadness of quantum correlations [6]. In analogy with the case of entanglement, the relation between quantum discord and the features of quantum many-body models is fundamentally interesting for the understanding of the role that the settlement of quantumness of correlations play in determining the critical properties of such models. A systematic analysis in this sense, which has only recently been considered [7][8][9][10][11][12][13], is thus highly desirable. This is even more important given that some of the investigations performed so far have indicated that quantum discord is more sensible than entanglement in revealing quantum critical points [9], even for systems that are not at zero temperature [14]. This is a particularly relevant result, whose validity should also be checked for models that are both finite sized and at finite temperature. The motivations for such an endeavor stem from the fact that, likely, the properties of quantum many-body systems will be addressed experimentally in systems consisting of, for instance, cold atoms loaded in optica...

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confidence: 95%

Global quantum correlations in finite-size spin chains

et al. 2013

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“…Discord has also been studied in the ground state of certain spin chains particularly close to quantum phase transitions [55]. Signatures of chaos in the dynamics of quantum discord are found using the model of the quantum kicked top [56].…”

Section: Quantum Discordmentioning

confidence: 99%

Quantum Correlations in NMR Systems

Mahesh¹,

Kumar²,

Bhosale³

2017

Quantum Science and Technology

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In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin ensembles are much lower than their thermal energies, and accordingly exhibit tiny polarizations.Generally such low-purity quantum states are devoid of quantum entanglement. However, there exist certain nonclassical correlations which can be observed even in such systems. In this chapter, we discuss three such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal correlations, and quantum discord. In each case, we provide a brief theoretical background and then describe some results from NMR experiments. * mahesh.ts@iiserpune.ac.in † sudheer.kumar@students.iiserpune.ac.in ‡ uday.bhosale@iiserpune.ac.in arXiv:1608.06579v1 [quant-ph] 5 Aug 2016 'Correlations cry out for explanation' -J. S. Bell in Speakable and Unspeakable in Quantum Mechanics, Cambridge university press (1989).

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“…These states represent, for example, the general form of reduced density operators of arbitrary quantum spin chains with Z 2 (parity) symmetry (for a review see, e.g., Ref. [20]). The trace-norm correlation measures have been analytically developed for a general X state [37,38], reading…”

Section: Applicationsmentioning

confidence: 99%

Non-Markovianity through multipartite correlation measures

2016

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We provide a characterization of memory effects in non-Markovian system-bath interactions from a quantum information perspective. More specifically, we establish sufficient conditions for which generalized measures of multipartite quantum, classical, and total correlations can be used to quantify the degree of non-Markovianity of a local quantum decohering process. We illustrate our results by considering the dynamical behavior of the trace-distance correlations in multi-qubit systems under local dephasing and generalized amplitude damping.

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Quantum Discord in the Ground State of Spin Chains

Cited by 47 publications

References 94 publications

Global quantum correlations in finite-size spin chains

Global quantum correlations in finite-size spin chains

Quantum Correlations in NMR Systems

Non-Markovianity through multipartite correlation measures

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