Quantum correlations in a family of bipartite separable qubit states

We investigate the behavior of quantum correlations in some specific Werner-like two-qubit states, where the qubit interacts individually with non-Markovian environment. We employ the local quantum uncertainty and trace distance discord to quantify the amount of quantum correlations between the evolved qubits and the corresponding analytical expressions are derived. For specific values of the parameters characterizing the whole system, the dynamics of quantum correlations exhibits collapse and revival phenomena. The influence of the non-Markovianity is also investigated to analyze the monotonic decay of quantum correlations in the limiting case of Markovian regime. Furthermore, we show that trace distance discord captures quantum correlations that cannot be revealed by local quantum uncertainty in some particular situations.

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Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations

Journal of the Optical Society of America B ◽

10.1364/josab.384936 ◽

2020 ◽

Vol 37 (4) ◽

pp. 1224

Author(s):

Nilakantha Meher ◽

Abu Saleh Musa Patoary ◽

Girish Kulkarni ◽

Anand K. Jha

Keyword(s):

Quantum Correlations ◽

Degree Of Coherence ◽

Qubit States

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A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schrödinger cat states

International Journal of Modern Physics B ◽

10.1142/s0217979215501246 ◽

2015 ◽

Vol 29 (19) ◽

pp. 1550124 ◽

Cited By ~ 1

Author(s):

M. Daoud ◽

R. Ahl Laamara ◽

S. Seddik

Keyword(s):

Quantum Discord ◽

Quantum Correlations ◽

Correlation Matrices ◽

Pairwise Correlation ◽

Logical Qubits ◽

Schrödinger Cat ◽

Cat States ◽

Qubit States ◽

Symmetric States ◽

Recursive Relations

A recursive approach to determine the Hilbert–Schmidt measure of pairwise quantum discord in a special class of symmetric states of k qubits is presented. We especially focus on the reduced states of k qubits obtained from a balanced superposition of symmetric n-qubit states (multiqubit Schrödinger cat states) by tracing out n-k particles (k = 2, 3, …, n-1). Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the parity grouping (k-1) qubits is explicitly derived. This uses recursive relations between the Fano–Bloch correlation matrices associated with subsystems comprising k, k-1, … and two particles. A detailed analysis is given for two-, three- and four-qubit systems. In the second scheme, the subsystem comprising the (k-1) qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multiqubits systems. The explicit expressions of classical states presenting zero discord are derived.

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THERMAL DISCORD AND NEGATIVITY IN A TWO-SPIN-QUTRIT SYSTEM UNDER DIFFERENT MAGNETIC FIELDS

International Journal of Quantum Information ◽

10.1142/s0219749913500706 ◽

2013 ◽

Vol 11 (08) ◽

pp. 1350070 ◽

Cited By ~ 8

Author(s):

XIAO-JING LI ◽

HUI-HUI JI ◽

XI-WEN HOU

Keyword(s):

Magnetic Fields ◽

Quantum Discord ◽

Strong Field ◽

Quantum Correlations ◽

Mixed States ◽

Classical Correlation ◽

Lower Temperature ◽

Qubit States ◽

Quantum And Classical Correlations

The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.

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Quantum correlations dynamics of three-qubit states coupled to an XY spin chain: Role of coupling strengths

Chinese Physics B ◽

10.1088/1674-1056/26/10/100501 ◽

2017 ◽

Vol 26 (10) ◽

pp. 100501 ◽

Cited By ~ 2

Author(s):

Shao-Ying Yin ◽

Qing-Xin Liu ◽

Jie Song ◽

Xue-Xin Xu ◽

Ke-Ya Zhou ◽

...

Keyword(s):

Spin Chain ◽

Quantum Correlations ◽

Coupling Strengths ◽

Xy Spin Chain ◽

Qubit States

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Quantum correlations of three-qubit states driven by a classical random external field

Physica Scripta ◽

10.1088/0031-8949/90/3/035103 ◽

2015 ◽

Vol 90 (3) ◽

pp. 035103 ◽

Cited By ~ 6

Author(s):

Youneng Guo ◽

Maofa Fang ◽

Shiyang Zhang ◽

Xiang Liu

Keyword(s):

External Field ◽

Quantum Correlations ◽

Qubit States ◽

Random External Field

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Condition for zero and nonzero discord in graph Laplacian quantum states

International Journal of Quantum Information ◽

10.1142/s0219749919500187 ◽

2019 ◽

Vol 17 (02) ◽

pp. 1950018 ◽

Cited By ~ 2

Author(s):

Supriyo Dutta ◽

Bibhas Adhikari ◽

Subhashish Banerjee

Keyword(s):

Quantum Mechanics ◽

Quantum Discord ◽

Graph Laplacian ◽

Quantum Correlations ◽

Quantum States ◽

Simple Graphs ◽

Graph Theoretic ◽

Weighted Directed Graph ◽

Special Case ◽

Qubit States

This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corresponding to a diverse class of quantum states. To this effect, we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and call them graph Laplacian quantum states. We find the graph theoretic conditions for zero and nonzero quantum discord for these states. We apply these results on some important pure two qubit states, as well as a number of mixed quantum states, such as the Werner, Isotropic, and [Formula: see text]-states. We also consider graph Laplacian states corresponding to simple graphs as a special case.

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Correlations in Two-Qubit Systems under Non-Dissipative Decoherence

Axioms ◽

10.3390/axioms9010020 ◽

2020 ◽

Vol 9 (1) ◽

pp. 20

Author(s):

Diego G. Bussandri ◽

Tristán M. Osán ◽

Pedro W. Lamberti ◽

Ana P. Majtey

Keyword(s):

Mutual Information ◽

Quantum Discord ◽

Quantum Correlations ◽

The Other ◽

Standard Quantum ◽

Optimal Value ◽

Quantum Mutual Information ◽

Classical Correlations ◽

Correlation Measures ◽

Qubit States

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

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