Quantum entanglement and quantum discord in magnetoactive materials (Review Article)

Алдошин, С. М.; Fel’dman, É. B.; Yurishchev, M. A.

doi:10.1063/1.4862469

Cited by 43 publications

(66 citation statements)

References 91 publications

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“…The quantum entanglement and quantum discord are invariant under the local unitary transformations of density matrices [1][2][3][4][5]. Owing to this property, one can with the help of such transformations reduce the sevenparameters density matrix to the real, nonnegative five-parameters X form [22][23][24][25].…”

Section: Real Nonnegative Form For the X Density Matrices And The Dommentioning

confidence: 99%

On the quantum discord of general X states

Yurischev

2015

Quantum Inf Process

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Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms (Q_{\pi/2} and Q_0) and an intermediate subdomain for which, to extract the quantum discord Q_\theta, it is required to solve in general numerically a one-dimensional minimization problem to find the optimal measurement angle \theta\in(0,\pi/2). Hence the quantum discord is given by a piecewise-analytic-numerical formula Q=\min{Q_{\pi/2}, Q_\theta, Q_0}. Equations for determining the boundaries between these subdomains are obtained. The boundaries consist of bifurcation points. The Q_{\theta} subdomains are discovered in the generalized Horodecki states, in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, in the heteronuclear dimers in an external magnetic field. We found that transitions between Q_{\theta} subdomain and Q_{\pi/2} and Q_0 ones occur suddenly but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher derivatives of discord function.Comment: 23 pages, 12 figures. arXiv admin note: text overlap with arXiv:1404.573

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Section: Real Nonnegative Form For the X Density Matrices And The Dommentioning

confidence: 99%

On the quantum discord of general X states

Yurischev

2015

Quantum Inf Process

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“…Let us discuss the behavior of the quantum discord at a large number of molecules in a nanopore. Figures 6 and 7 show the time variations of the discord at N = 20 and 10 3 . We see that the maxima of the curves become flat and their magnitudes approach the thermody namic limit (58) with increasing N. In this case, the relative extents of the horizontal plateaus (saturation regions) increase, while the time intervals between them when the correlations drop to zero decrease.…”

Section: The Real X Form Of a Two Particle Density Matrixmentioning

confidence: 99%

“…Using the Bayes formula known in the probability theory, the right part of equality (2) for the mutual information can be written in Shannon's nonsymmet ric form that we will denote by : (3) where (4) is the conditional entropy. In the classical case, of course, ≡ Ᏽ.…”

Section: Correlations and Their Measuresmentioning

confidence: 99%

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NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore

Yurishchev

2014

J. Exp. Theor. Phys.

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Previously [22], we made an attempt to theoreti cally study the dynamical quantum correlations in a model of N moving I = 1/2 spins confined in the pres ence of a strong magnetic field B 0 in a volume with an Abstract-A local orthogonal transformation that transforms any centrosymmetric density matrix of a two qubit system to the X form has been found. A piecewise analytic-numerical formula Q = min{Q π/2 , Q θ , Q 0 }, where Q π/2 and Q 0 are analytical expressions and the branch Q θ can be obtained only by numerically searching for the optimal measurement angle θ ∈ (0, π/2), is proposed to calculate the quantum discord Q of a general X state. The developed approaches have been applied for a quantitative description of the recently predicted flickering (periodic disappearance and reappearance) of the quantum information pair correlation between nuclear 1/2 spins of atoms or molecules of a gas (for example, 129 Xe) in a bounded volume in the presence of a strong magnetic field.

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“…This fact stimulated alternative measurements of quantum discord, theoretically and experimentally [22,24,29,[34][35][36]. The recent demonstration that quantum discord can be measured by the thermodynamic properties of solids, such as magnetic susceptibility, internal energy [35][36][37], specific heat [35,36] and even neutron scattering data [22], shows that quantum correlations can be related to significant macroscopic effects allowing the measurement and the control of quantum correlations in solid state systems by means of material engineering. Thus, the design of novel materials becomes an actual challenge to overcome.…”

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confidence: 99%

Carboxylate-based molecular magnet: One path toward achieving stable quantum correlations at room temperature

Cruz¹,

Soares-Pinto²,

Brandão³

et al. 2016

EPL

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The control of quantum correlations in solid state systems by means of material engineering is a broad avenue to be explored, since it makes possible steps toward the limits of quantum mechanics and the design of novel materials with applications on emerging quantum technologies. In this context, this Letter explores the potential of molecular magnets to be prototypes of materials for quantum information technology. More precisely, we engineered a material and from its geometric quantum discord we found significant quantum correlations up to 9540 K (even without entanglement); and, in addition, a pure singlet state occupied up to around 80 K (above liquid nitrogen temperature). These results could only be achieved due to the carboxylate group promoting a metal-to-metal huge magnetic interaction. Keywords: Quantum discord, Geometric correlations, Molecular magnetsQuantum entanglement has received a considerable attention as a remarkable resource for quantum information processing [1][2][3]. In spite of that, it is fragile and can easily vanish due to the inevitable interaction of the system with its environment [4]; and due to this condition, it was thought that entanglement could only exist at low temperatures. However, recently, it has been shown that entanglement can also exist at higher temperatures, and can be detected through the measurement of some thermodynamic observables [5][6][7][8][9][10][11][12][13][14][15][16][17].Nevertheless, quantum entanglement does not encompass all quantum correlations in a system and recent studies have greatly expanded the notion of quantum correlations [18][19][20][21][22][23][24][25][26][27][28][29]; and the measure of quantum excess of correlations has been named as quantum discord [19][20][21]. In the last years, it was understood that quantum discord has an important role in many quantum information processing even without entanglement. Notably, this quantity can also detect quantum phase transitions [25,30,31].Despite much effort by the scientific community, there are only a few results on the analytical expression of quantum discord; and only for a certain class of states an exact solution is known [23-27, 32, 33]. This fact stimulated alternative measurements of quantum discord, theoretically and experimentally [22,24,29,[34][35][36]. The recent demonstration that quantum discord can be measured by the thermodynamic properties of solids, such as magnetic susceptibility, internal energy [35][36][37], specific heat [35,36] and even neutron scattering data [22], shows that quantum correlations can be related to significant macroscopic effects allowing the measurement and the control of quantum correlations in solid state systems by means of material engineering. Thus, the design of novel materials becomes an actual challenge to overcome.In this direction, molecular magnets can be an excellent opportunity to achieve this goal as prototypes of materials for quantum information technology. They combine classical properties, found in any macroscopic magnet, with quantum one...

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Quantum entanglement and quantum discord in magnetoactive materials (Review Article)

Cited by 43 publications

References 91 publications

On the quantum discord of general X states

On the quantum discord of general X states

NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore

Carboxylate-based molecular magnet: One path toward achieving stable quantum correlations at room temperature

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