Quantum correlations in topological quantum phase transitions

Chen, Yixin; Li, Sheng-Wen

doi:10.1103/physreva.81.032120

Cited by 100 publications

(47 citation statements)

References 23 publications

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“…Meanwhile, the nonclassical correlation is measured by the so-called quantum discord [3], which is the difference of the total amount of correlations and the classical correlation. Over the past decade, quantum discord has received a good amount of attention, including analytic calculations for some special two-qubit states [4,5], detecting of quantum discord [6][7][8][9][10][11][12][13], quantum discord in the concrete physical models [14][15][16][17][18][19][20][21][22][23], the dynamics of quantum discord [24][25][26][27][28][29][30][31][32][33][34][35], quantum discord in continuous variable systems [36,37], quantum discord of multipartite states [38], and exploration in the laboratory [39][40][41], etc. Most recently, operational interpretations of quantum discord are proposed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Optimal measurements to access classical correlations of two-qubit states

et al. 2011

Phys. Rev. A

153

138

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We analyze the optimal measurements to access classical correlations in arbitrary two-qubit states. Two-qubit states can be transformed into the canonical forms via local unitary operations. For the canonical forms, we investigate the probability distribution of the optimal measurements. The probability distribution of the optimal measurements is found to be centralized in the vicinity of a specific von Neumann measurement, which we call the maximal-correlation-direction measurement (MCDM). We prove that, for the states with zero discord and maximally mixed marginals, the MCDM is the optimal measurement. Furthermore, we give an upper bound of quantum discord based on the MCDM, and investigate its performance for approximating the quantum discord.

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Section: Introductionmentioning

confidence: 99%

Optimal measurements to access classical correlations of two-qubit states

et al. 2011

Phys. Rev. A

153

138

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“…We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.plays an important role in identifying quantum phase transitions [8,20], quantum discord has received much attention in this regard as well [21,22]. Moreover, it was applied in several contexts like open quantum systems [23], quantum dynamics [24] and even biophysics [25].Recently, the concept of quantum coherence has received much attention in the quantum information community as it plays an essential role in phenomena like quantum interference, bipartite and multipartite entanglement [26].…”

mentioning

confidence: 99%

“…plays an important role in identifying quantum phase transitions [8,20], quantum discord has received much attention in this regard as well [21,22]. Moreover, it was applied in several contexts like open quantum systems [23], quantum dynamics [24] and even biophysics [25].…”

mentioning

confidence: 99%

Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain

Mzaouali

Baz

2019

Physica A: Statistical Mechanics and its Applications

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A comparative study of pairwise quantum coherence, quantum and classical correlations is addressed for non-nearest spin pairs of the 1D Heisenberg spin-1 2 XX chain. Following the Jordan-Wigner mapping, we diagonalise the hamiltonian of the chain and we check this procedure numerically as well. Using the "Pauli basis expansion" formalism we get the pairwise quantities studied in this work at any distance. We then, show the role of quantum correlations in revealing quantum phase transitions, the robustness of quantum discord to the temperature and the dominance of quantum correlations over their classical counterpart in the magnetic and thermal interval in quantum spin chains. We conclude the paper by shedding light from a resource-driven point of view on the new born quantity "quantum coherence" where we discuss its role in detecting quantum phase transitions being a long-range quantity, and how it outclasses the usual quantum correlations measures in the robustness against the temperature, which indicates potential uses in the framework of quantum information processing.plays an important role in identifying quantum phase transitions [8,20], quantum discord has received much attention in this regard as well [21,22]. Moreover, it was applied in several contexts like open quantum systems [23], quantum dynamics [24] and even biophysics [25].Recently, the concept of quantum coherence has received much attention in the quantum information community as it plays an essential role in phenomena like quantum interference, bipartite and multipartite entanglement [26]. Various schemes were proposed for detecting coherence [27,28], but it was never quantified in the language of quantum information theory until the seminal work of Baumgratz, Cramer and Plenio [29] in which they constructed a quantitative theory that captures the resource character of coherence in a mathematically rigorous fashion. Such developments led to number of applications using coherence as a basic ingredient in various fields such as quantum communication [30] and in farther other arenas, such as thermodynamics [31] and even certain branches of biology [32]. Few works were dedicated to study quantum coherence in condensed matter systems [33,34,35,36]. In fact, the investigations that were carried out in spin chains like the XY model had the sole purpose of revealing the connection between quantum coherence and quantum phase transitions. These studies has shown the role played by coherence in detecting important features like critical points, but it is still early to say how efficient quantum coherence is in detecting quantum phase transitions as the field needs more models and measures to investigate these connections.Motivated by these developments, the aim of this paper is to study and compare the behavior of non-nearest quantum coherence, quantum and classical correlations in an infinite 1D spin-1 2 XX chain in the presence of a magnetic field. This is an analytically solvable model by means of the Jordan-Wigner transformation which we check numeric...

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“…Only when the QD disappears, the information can be safely obtained by locally measuring the distantly separate subsystem without disturbing the bipartite quantum system, where the corresponding state is fully classical. Recently, the QD has successfully been used to study the quantum phase transition of the critical systems [17][18][19][20][21][22], operational meanings for quantum processors [23] and state preparation [24].…”

Section: Introductionmentioning

confidence: 99%

Exact dynamics of quantum correlations of two qubits coupled to bosonic baths

Wang

Chen

2013

New J. Phys.

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Dynamics of the quantum entanglement and quantum discord of two qubits in two independent baths and a common bath with the Lorentzian spectrum are studied exactly in the numerical sense within the hierarchy approach. The effects of the counter-rotating-wave terms from the system-bath coherence on these quantum correlations are systematically discussed and comparisons with previous ones under the rotating-wave approximation are also performed. For two independent baths, beyond the weak system-bath coupling, the counter-rotating-wave terms essentially change evolutions of both the entanglement and quantum discord. With increase of the coupling, revival of the entanglement after a period of complete disentanglement is suppressed dramatically and finally disappears, and the quantum discord becomes smaller monotonically. For the common bath, the entanglement is also suppressed by the counter-rotating-wave terms, but the quantum discord shows quite different behaviors if initiated from spin-correlated states. In the non-Markovian regime, the quantum discord is almost not influenced by the counter-rotating-wave terms and is generally finite in the long-time evolution at arbitrary coupling while in the Markovian regime, it is significantly enhanced with the strong coupling.

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Quantum correlations in topological quantum phase transitions

Cited by 100 publications

References 23 publications

Optimal measurements to access classical correlations of two-qubit states

Optimal measurements to access classical correlations of two-qubit states

Long range quantum coherence, quantum & classical correlations in Heisenberg XX chain

Exact dynamics of quantum correlations of two qubits coupled to bosonic baths

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