Pairwise Quantum Correlations Research Articles

Thermal quantum correlations in a two-qubit Heisenberg model under Calogero–Moser and Dzyaloshinsky–Moriya interactions

In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.

Local quantum uncertainty versus negativity through Gisin states

We investigate the pairwise quantum correlations in standard Gisin states and in Gisin states based on bipartite spin-coherent states by employing quantum negativity and quantum local uncertainty as bona fide quantum correlations measures. Gisin states are defined as mixtures of separable mixed states and some pure entangled ones. We compare the behavior of the two quantifiers of Gisin states and we find that both measures exhibit a sudden change in terms of the mixing parameter. Furthermore, we show that entangled Gisin states contain nonclassical correlations that are captured by the local quantum uncertainty and cannot be revealed by the negativity quantifier.

Pairwise quantum correlations in four-level quantum dot systems

In this paper we assume quantum dots can be assimilated to Fermi Hubbard sites when the Coulomb interaction between electrons is higher compared to their tunneling. The study of pairwise entanglement in a small size array of quantum dots allows to model each pair as a quadrit-quadrit system (4 × 4 mixed state) instead of the more common and simplistic approach of describing it in quantum information as a qubit-qubit system. We study the effect of Coulomb interaction and temperature on pairwise entanglement as well as on quantum coherence and total correlations. The crucial results of this study are that entanglement resists better the increase in temperature when the Coulomb interaction is stronger. Moreover, we successfully explain the behavior of these correlations in terms of the energy spectrum, namely the ground state degeneracy and the state energy difference.

The pairwise quantum correlations for teleported state via a symmetric multi-qubit system

We study the pairwise quantum correlations for teleported state via a symmetric multi-qubitsystem. In the other words, the proposed model is considered as a quantum channel. Using thequantum discord, super quantum discord and concurrence to quantify quantum correlations forteleported state, some analytical and numerical results are presented. Moreover, we compare thedynamical evolutions of quantum correlations and fidelity versus measurement strength and thenumber of qubit channel for teleported state via symmetric multi-qubit model. Our main goalnow is to study how we can increase the quantum correlations and the fidelity of the teleportedstate in the presence of decoherence. The results show that, measurement strength and thenumber of qubit can control the quantum information obtained through the quantum channel.Therefore, measurement strength can be a good option for measuring exchanged information inthe teleportation process. In addition to, quantum correlations can provide an effective role inquantum teleportation

Experimental verification of anisotropic invariance for three-qubit states

We experimentally test the recently predicted anisotropic invariance properties of pure three-qubit states, via generation and measurement of polarisation-path entangled three-qubit states. These properties do not require aligned reference frames and can be determined from measurements on any two of the qubits. They have several applications, such as a universal ordering of pairwise quantum correlations, strong monogamy relations for Bell inequalities and quantum steering, and a complementarity relation for Bell nonlocality versus 3-tangle, some of which we also test. The results indicate that anisotropic invariance, together with the three qubit Bloch vector lengths, can provide a robust and complete set of invariants for such states under local unitary transformations.

Many-body localization transition through pairwise correlations

We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction $J$ and random onsite disorder of strength $h$. As a representative pairwise correlation measure obtained from one-point functions only, we use global entanglement. Through its finite size scaling analysis, we locate the MBL critical point at $h_{c}/J = 3.8$. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range $h_{c}/J \in \left[3,4\right]$. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.

Quantum correlations for two-qubit X states through the local quantum uncertainty

Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.

Nonclassical correlations in a two-mode optomechanical system

The pairwise quantum correlations in a tripartite optomechanical system comprising a mechanical mode and two optical modes are analyzed. The Simon criterion is used as a witness of the separability. Whereas the Gaussian discord is employed to capture the quantumness of correlations. Both entanglement and Gaussian discord are evaluated as functions of the parameters characterizing the environment and the system (temperature, squeezing and optomechanical coupling). We work in the resolved-sideband regime. We show that it is possible to reach three simultaneous bipartite entanglements via the quantum correlations transfer from the squeezed light to the system. While, even without squeezed light, the quantumness of correlations can be captured simultaneously between the three modes for a very wide range of parameters. Specifically, we find that the two optical modes exhibit more quantum correlations in comparison with the entangled mechanical–optical modes. Finally, unlike the two hybrid subsystems, the purely optical one seems more resilient against the environmental destructive effects.

Distribution of geometric quantum discord in photon-added coherent states

In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger–Horne–Zeilinger (GHZ) type. The Hilbert–Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.

Hilbert–Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit $X$ states. They include three-qubit states of ${\rm W}$, ${\rm GHZ}$ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system

In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.

Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy

The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum–classical and quantum–classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined.

Correlations and Werner states in finite spin linear arrays

Pairwise quantum correlations in the ground state of an N-spins antiferromagnetic Heisenberg chain are investigated. By varying the exchange coupling between two neighboring sites, it is possible to reversibly drive spins from entangled to disentangled states. For even N, the two-spin density matrix is written in the form of a Werner state, allowing identification of its single parameter with the usual spin-spin correlation function. The N = 4 chain is identified as a promising system for practical demonstrations of non-classical correlations and the realization of Werner states in familiar condensed matter systems. Fabrication and measurement ingredients are within current capabilities.

Multipartite quantum correlations in even and odd spin coherent states

The key ingredient of the approach presented in this paper is the factorization property of SU(2) coherent states upon the splitting or decay of a quantum spin system. In this picture, the even and odd spin coherent states are viewed as comprising two, three or more spin sub-systems. From this perspective, we investigate the multipartite quantum correlations defined as the sum of the correlations of all possible bi-partitions. The pairwise quantum correlations are quantified by entanglement of formation and quantum discord. Special attention is devoted to tripartite splitting schemes. We explicitly derive the sum of the entanglement of formation for all possible bi-partitions. It coincides with the sum of all possible occurrences of pairwise quantum discord. The conservation relation between the distribution of entanglement of formation and quantum discord in the tripartite splitting scheme is discussed. We show that entanglement of formation and quantum discord possess the monogamy property for even spin coherent states, in contrast to odd ones which violate the monogamy relation when the overlap of the coherent states approaches unity.

Generalized entropy and global quantum discord in multiparty quantum systems

Using Tsallis-$q$ entropy, we introduce the generalized concept of global quantum discord, namely the $q$-global quantum discord, and provide its analytic evaluation for two classes of multiqubit states. We also provide a sufficient condition, for which the pairwise quantum correlations in terms of $q$-global quantum discord is monogamous in multiparty quantum systems.

Genuine correlations of tripartite system

We define genuine total, classical and quantum correlations in tripartite systems. The genuine tripartite quantum discord can be interpreted as ‘quantum advantage’ in tripartite superdense coding. We find in a symmetrical tripartite state, for total correlation and classical correlation, the genuine tripartite correlations are no less than the pair-wise correlations. However, the genuine quantum tripartite correlation can be surpassed by the pair-wise quantum correlations. Analytical expressions for genuine tripartite correlations are obtained for pure states and rank-2 symmetrical states. The genuine correlations in both entangled and separable states are calculated.

Monogamy of quantum discord by multipartite correlations

We introduce a monogamy inequality for quantum correlations, which implies that the sum of pairwise quantum correlations is upper limited by the amount of multipartite quantum correlations as measured by the global quantum discord. This monogamy bound holds either for pure or mixed quantum states provided that bipartite quantum discord does not increase under discard of subsystems. We illustrate the monogamy behavior for multipartite pure states with Schmidt decomposition as well as for $W$-GHZ mixed states. As a by-product, we apply the monogamy bound to investigate residual multipartite correlations.

Pairwise quantum correlations of a three-qubit XY chain with phase decoherence

Quantum correlations, including entanglement and discord with its geometric measure in a three-qubit Heisenberg XY chain, with phase decoherence, are investigated when a nonuniform magnetic field is applied. When the qubits are initially in an unentangled state, the nearest neighbor pairwise correlations are destroyed by phase decoherence, but stationary correlations appear for next-to-neighbor qubits. With an inhomogeneous magnetic field, the stationary correlations appear for nearest neighbor qubits and they disappear for next-to-nearest neighbor qubits. But when the qubits are initially in an entangled state, an inhomogeneous magnetic field can enhance the stationary correlations of next-to-neighbor qubits, but it cannot do so for nearest neighbor qubits. The decoherence effect on stationary correlations is much stronger for next-to-nearest neighbor qubits than it is for nearest neighbor qubits. Finally, a uniform magnetic field can affect the correlations when the qubits are initially in an entangled state, but it cannot affect them when the qubits are initially in an unentangled state.

Quantum discord of Bell cat states under amplitude damping

The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi–Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.