Local Quantum Uncertainty Research Articles

Fisher and Skew Information Correlations of Two Coupled Trapped Ions: Intrinsic Decoherence and Lamb-Dicke Nonlinearity

It is well known that many quantum information processing methods in artificial atoms depend largely on their engineering properties and their ability to generate quantum correlations. In this paper, we investigate the non-classical correlation dynamics of two trapped ions by using local quantum Fisher information, local quantum uncertainty, as well as logarithmic negativity. The system engineering is designed such that the two-trapped-ions work as two diploe-coupled qubits in a Lamb-Dicke regime. The center-of-mass vibrational modes are initially in coherent/even coherent states. It is found that the two-trapped-ions correlations can be controlled by the Lamb-Dicke nonlinearity, the nonclassicality effect of the initial center-of-mass vibrational mode, as well as the trapped-ion coupling and the intrinsic decoherence. The sudden changes in the non-classical correlations and their stability are shown against Lamb-Dicke nonlinearity, the nonclassicality, the trapped-ion coupling, and the intrinsic decoherence.

Local two-atom correlations induced by a two-mode cavity under nonlinear media: Quantum uncertainty and quantum Fisher information

The nonlinearity effect on the various formed quantum correlations between two atoms interacting locally with a bimodal cavity is explored in this work. The local quantum Fisher information, local quantum uncertainty, and negativity are used to investigate the quantum correlation’s sensitivity to the cavity modes characteristics. It is demonstrated that when the ratio of the Stark shift of the two modes increases, the atomic quantum correlations rise. During the time intervals of sudden death negativity entanglement, the three two-atom correlation quantifiers reveal that the two-atom system can contain local Fisher information and local uncertainty correlations. The Stark shift may be utilized to amplify the produced atomic correlation, while the Kerr-like medium can be used to suppress it. The regularity, the amount of generated atomic correlations, and their immunity to the Stark shift as well as the Kerr-like medium non-linearities are improved when the mean photon number is increased. As a result, the cavity modes’ nonlinear parameters might be utilized as a controller to optimize atomic quantum correlations.

Effects of intrinsic decoherence on discord-like correlation measures of two-qubit spin squeezing model

Quantum decoherence happens when the system interacts with the environment. Quantum correlation behaviours in the two-qubit spin squeezing model are studied under the influence of intrinsic decoherence. Quantitative results were determined, which depend on parameters of the physical system by checking different quantifiers of quantum correlation such as entanglement, local quantum uncertainty, trace distance discord and uncertainty-induced quantum nonlocality. We show that the entanglement suffers from intrinsic decoherence and exhibits sudden death, whereas the other measures are more robust against intrinsic decoherence. Further, we highlight the role of spin squeezing coupling constant and magnetic field.

The accelerated Gisin state: its non-locality, quantum correlations and efficiency to perform quantum masking

The local and non local behavior of the accelerated Gisin state are investigated either before or after filtering process. It is shown that, the possibility of predicting the non-local behavior is forseen at large values of the weight of the Gisin and acceleration parameters. Due to the filtering process, the non-locality behavior of the Gisin state is predicted at small values of the weight parameter. The amount of non classical correlations are quantified by means of the local quantum uncertainty (LQU)and the concurrence, where the LQU is more sensitive to the non-locality than the concurrence. The phenomenon of the sudden changes is displayed for both quantifiers. Our results show that, the accelerated Gisin state could be used to mask information, where all the possible partitions of the masked state satisfy the masking criteria. Moreover, there is a set of states, which satisfy the masking condition, that is generated between each qubit and its masker qubit. For this set, the amount of the non-classical correlations increases as the acceleration parameter increases . Further, the filtering process improves these correlations, where their maximum bounds are much larger than those depicted for non-filtered states.

Quantum Fisher information and skew information correlations in dipolar spin system

Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair of spin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local quantum Fisher information (lQFI). The effects of dipolar coupling constants on quantum correlation quantifiers are studied. The DM interaction greatly enhances the quantum correlation in the system whereas the temperature tends to annihilate the amount of quantum correlations.

Local Fisher- and skew-information coherence of two Nitrogen-Vacancy centers induced by two coupled dissipative nanocavities

The paper investigates the dynamics of the quantum interferometric power and Local quantum uncertainty coherences beyond concurrence entanglement between two Nitrogen-Vacancy centers (NVCs) induced by two coupled dissipative nanocavities. A particular engineering design is considered, where each nanocavity contains a coherently driven N-V center and the two nanocavities are initially in a maximally correlated state with different initial two-NVC states. It is found that, for the initial uncorrelated two-NVC state, the generated two-NVC coherence and the entanglement due to the NVC-nanocavity interactions can be enhanced by the increase of the Nitrogen-Vacancy center’s couplings. The cavity dissipations enhance the generation of Fisher and skew information quantumness of the two-NVC state, and accelerate the reduction of the concurrence entanglement. For the initial maximally correlated two-NVC state, the robustness of the two-NVC coherence and the entanglement against the NVC-nanocavity interactions and the dissipation can be enhanced by the two-nanocavity coupling and the two NVC-qubits couplings.

Equivalence regimes for geometric quantum discord and local quantum uncertainty

The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Phys. Rev. Lett 88, 017901 (2002)] is difficult to compute even for the simplest case of two-qubits systems. Alternative formulations have been developed to address this drawback, such as the geometric measure of quantum discord [Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [Phys. Rev. Lett 110, 240402 (2013)] that can be evaluated in closed form for some quantum systems, such as two-qubit systems. We show here that these two measures of quantum discord are equivalent for 2 x D dimensional bipartite quantum systems. By considering the relevant example of N00N states for phase estimation in lossy environments, we also show that both metrics of quantum discord quantify the decrease of quantum Fisher information of the phase estimation protocol. Given their ease of computation in 2 x D bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord.

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.

Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty

Nonclassical correlations in two-qubit Ising model with an arbitrary magnetic field: Local quantum Fisher information and local quantum uncertainty

Local quantum uncertainty in a two-qubit Heisenberg spin chain with intrinsic decoherence

Quantum correlation plays an important role in quantum information processing, for which various quantifiers have been proposed so far. In this paper, we address the dynamics of local quantum uncertainty (LQU) as a reliable quantifier of quantum correlation in a two-qubit Heisenberg spin chain in the presence of nonuniform external magnetic field and Dzyaloshinski-Moriya interaction with intrinsic decoherence. The influences of the initial states, external magnetic field strength, Dzyaloshinski-Moriya interaction strength and intrinsic decoherence rate on the dynamics of LQU have been in detail investigated. Our analytical results show that the dynamics of LQU is strongly depended on the form of initial states. For an initial correlated state, the dynamical behaviors of LQU exhibit either monotonic decay or damped oscillations with respect to time. While for an initial separable state, quantum correlation quantified by LQU can be created due to the Dzyaloshinski-Moriya interaction and Heisenberg anisotropic interaction. Besides, the relationship between LQU and l-norm coherence or concurrence is also demonstrated in the present model.

Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii–Moriya interaction

By taking into account the effect of intrinsic decoherence and by using Milburn’s dynamical master equation, we study the temporal evolution of quantum correlations in a two-qubit XXZ Heisenberg spin chain model with Dzyaloshinskii–Moriya (DM) interaction and an external nonuniform magnetic field both directed along the z-axis. We use the concurrence (C) to detect entanglement and the local quantum uncertainty (LQU) to measure discord-like correlations. We consider three cases of initial quantum states: the mixed state, the Werner state and the pure state. For the mixed initial state and the Werner initial state, our results show that the external magnetic field strongly stimulates the effect of intrinsic decoherence which can highlight the entanglement sudden death phenomenon, while the LQU is resistant to sudden death. In addition, the DM interaction makes the effect of intrinsic decoherence more pronounced. However, a weak DM interaction can markedly improve quantum correlations and thus cause the phenomenon of entanglement sudden revival. On the other hand, and especially for the initial “uncorrelated” state (in terms of entanglement and LQU) with a zero nonuniform magnetic field and no DM interaction, it is easier to generate a strong entanglement, but it is difficult to generate LQU. Finally, we have found that when the system is initially “uncorrelated,” the nonuniform magnetic field can make the system strongly correlated for very remarkable steady-state values (in particular entanglement). Other results will also be discussed.

On the thermal nonclassical correlations in a two-spin XYZ Heisenberg model with Dzyaloshinskii–Moriya interaction

The quantum correlations between two neighbouring anisotropic XYZ Heisenberg spins under the effect of Dzyaloshinskii–Moriya interaction at thermal equilibrium is considered. We evaluate and compare the negativity, uncertainty-induced quantum nonlocality and local quantum uncertainty corresponding to involved system. By exploiting the behaviour of each quantifier, in terms of the system parameters, we have shown that the uncertainty-induced quantum nonlocality can reveal certain non-classicality that goes beyond negativity and local quantum uncertainty. Further, we show that the presence of Dzyaloshinskii–Moriya interaction along the z-axis can reduce the undesirable destructive effects of thermal fluctuations, and therefore enhances quantum correlations in the two-spin system. In addition, an entangled–unentangled phase transition can be detected from the behaviour of negativity.

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.

Dynamics of local quantum uncertainty among cavity–reservoir qubits

We study dynamics of local quantum uncertainty (LQU) for a system of two cavities and two reservoirs. In the start, the cavities are treated as two qubits which are quantum correlated with each other, whereas reservoirs (also qubits) are neither correlated with each other nor with cavities. We answer two main questions in this work. First, how local quantum uncertainty decays from two quantum correlated cavities and grows among reservoirs. The second question is the examination of LQU developed among four qubits and also shed some light on its dynamics. We observe that LQU develops among reservoirs as kind of mirror image to its decay from cavities. For four qubits, we propose how to compute LQU such that the method is intuitive and analytically computable. We find that among four qubits, LQU starts growing from zero to some maximum value and then decays again to zero as the asymptotic state of cavities is completely transferred to reservoirs. We suggest the experimental setup to implement our results.

Dynamics of local quantum uncertainty and local quantum fisher information for a two-qubit system driven by classical phase noisy laser

In this paper, the dynamics of quantum correlation quantified by local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for two uncoupled qubits driven by classical phase noisy laser have been investigated. The results show that, both LQU and LQFI exhibit similar behaviours, either display exponential decay or oscillatory decay with revivals depending on the ratios of classical phase noisy laser rate and system-environment coupling strength. Beside, our results also confirm the amount of quantum correlation measured by LQU is strictly bounded by LQFI in an open system. Finally, we propose a scheme to protect quantum correlation against classical phase noisy laser with the technique of weak measurement and reversal.

Dynamics of two coupled qubits interacting with two-photon transitions via a nondegenerate parametric amplifier: nonlocal correlations under intrinsic decoherence

In this study, an analytical solution for a novel intrinsic noise model represented by two coupled qubits inside a cavity, the S u ( 1 , 1 ) and S u ( 2 ) Lie group, is investigated. Each qubit interacts with a two-mode parametric amplifier through a nondegenerate two-photon process when the two-mode system is initially in a superposition of a generalized Barut–Girardello coherent state. The nonlinearity of the interaction and the initial two-mode fields lead to the generation of different quantum correlations (QCs), which are measured by log-negativity, uncertainty-induced nonlocality, and local quantum uncertainty (LQU). The generated QC of the interaction depends not only on the two-qubit coupling but also on the intrinsic noise and the initial coherent intensity. Our results show that the ability of the two-qubit coupling to protect and enhance the robustness and generation of the QCs depends on the superposition and the coherent intensity of the initial S u ( 1 , 1 ) state. Furthermore, the sudden birth and death of the log-negativity and the sudden variations of the LQU depend on the intrinsic noise and the two-qubit coupling.

Local quantum uncertainty in a two-qubit system due to classical environmental noise

In this paper, we address the dynamics of nonclassical correlation, quantified by local quantum uncertainty (LQU) in a two-qubit system subjected to classical environmental noise when the initial states of system are prepared in a specific class of Bell states. Two different configurations of the local noisy environment are examined. In the first case, we consider a system of two independently qubits, each locally interacting with its classical random noise, whereas in the second case we consider only one of qubits subject to a classical random noise. Our results show that the dynamics of LQU is strongly related to both the dephasing and relaxation factors. The behaviors of LQU in above two cases exhibit similar variation, with monotonic decay in the weak coupling region, while revivals in the strong coupling region depending on the ratio of the switching rate and coupling strength to the qubit. By controlling this ratio, long-time survival of LQU is obtained. Therefore, our results may open an interesting perspective in using of the long-time survival of quantum correlations for practical applications in quantum information science.

Local quantum Fisher information and local quantum uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions

Quantum correlations play an important role in quantum information theory. Quantum Fisher information (QFI) via local observables and via local measurements (i.e. local QFI (LQFI)) is a fundamental concept in quantum estimation and quantum metrology. LQFI captures the quantumness of correlations in a multicomponent quantum system. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In this work we will study the LQFI and the LQU in the two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction in the z-direction. Here we show that the DM interaction and spin interactions along the x- and z-axes can increase and maintain LQFI and LQU. It is also shown that because of thermal fluctuations LQFI and LQU are decreased by increasing temperature. They are equal to one at very low temperature and start to decay only after a thereshold temperature.

Local quantum uncertainty for multipartite quantum systems

Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure over measurements. This measure is initially defined for bipartite quantum systems and a closed formula exists only for $2 \otimes d$ systems. We extend the idea of local quantum uncertainty to multi-qubit systems and provide the similar closed formula to compute this measure. We explicitly calculate local quantum uncertainty for various quantum states of three and four qubits, like GHZ state, W state, Dicke state, Cluster state, Singlet state, and Chi state all mixed with white noise. We compute this measure for some other well known three qubit quantum states as well. We show that for all such symmetric states, it is sufficient to apply measurements on any single qubit to compute this measure, whereas in general one has to apply measurements on all parties as local quantum uncertainties for each bipartition can be different for an arbitrary quantum state.

Sudden change of local quantum uncertainty and geometry for arbitrary two-qubit X-states

Local quantum uncertainty (LQU) as a reliable measure of nonclassical correlations has been recently proposed by Girolami et al. (Phys Rev Lett 110:240402, 2013). In this paper, we have derived an explicit analytical expression of LQU and presented the level surfaces of constant LQU for a class of two-qubit X-states beyond Bell-diagonal states. The dynamical behavior of quantum correlations via the LQU under decoherence environment is studied, and the phenomenon of a sudden change of LQU is demonstrated. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system where there is a necessary condition for the occurrence of sudden change of LQU.