Measurement-induced nonlocality in the W and Greenberger–Horne–Zeilinger superposition states

Measurement-induced nonlocality（MIN） is a newly defined quantity to measure correlations in bipartite quantum states [Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401]. MIN in the n-qubit W and Greenberger–Horne–Zeilinger（GHZ） superposition states is considered. It is revealed that n = 3 and n ≥ 4 states have very different characteristics,especially the monogamy relation about MIN, and the monogamy equality of MIN is held in all n-qubit W states（n ≥ 3）.

Measurement-induced disturbance and nonequilibrium thermal entanglement in a qutrit qubit mixed spin XXZ model

We investigate the dynamics of nonequilibrium thermal quantum correlation of a qutrit-qubit mixed spin system coupled to two bosonic reservoirs at different temperatures using measurement-induced disturbance. The effects of initial states of the spins and temperatures of the reservoirs on measurement-induced disturbance and entanglement are discussed. The results demonstrate that measurement-induced disturbance is more robust than entanglement against the influence of both these factors and there is no sudden death phenomenon for measurement-induced disturbance. The dependences of steady-state measurement-induced disturbance and entanglement on coupling constant and anisotropy parameter are also studied. Steady-state entanglement vanishes for a ferromagnetic qutrit-qubit model, while steady- state measurement-induced disturbance exists for both the antiferromagnetic and ferromagnetic cases. Appropriately modulating the coupling constant and anisotropy parameter can strengthen quantum correlation.

Measurement-induced disturbance in Heisenberg XY spin model with Dzialoshinskii-Moriya interaction under intrinsic decoherence

Quantum correlations measured by measurement-induced disturbance （MID） in a two-qubit Heisenberg XY spin model with Dzialoshinskii-Moriya （DM） interaction under intrinsic decoherence are investigated. MID is studied un-der various circumstances and the influences of the external dependencies on the final quantum state which has stable MID are discussed. Two kinds of initial quantum states are considered as well as different conclusions. MID appears to decay periodically during the processing of intrinsic decoherence; both DM interaction and intrinsic decoherence have a negative impact on the correlations. The MID of the stable state depends on several factors, except the parameter of the intrinsic decoherence. Moreover, we find a special initial state that is able to maintain the maximum quantum correlations during the processing of intrinsic decoherence.

Dynamics of measurement-induced non-locality and geometric discord with initial system-environment correlations

We analyze the dynamics of geometric measure of discord （GMOD） and measurement-induced non-locality （MIN） in the presence of initial system-reservoir correlations without Born and Markov approximation. Although the initial system-environment states have the same reduced density matrices for both the system and environment, the effects of different initial system-environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.

Measurement-induced disturbance between two atoms in Tavis-Cummings model with dipole dipole interaction

Quantum correlation, measured by measurement-induced disturbance （MID）, between two two-level atoms is investi- gated in detail in Tavis-Cummings model with dipole--dipole interaction （DDI）. We find that MID can be determined only by the dipole-dipole interaction between the two atoms when the cavity and atoms are at resonance. Moreover, DDI will have different effects on MID for two different kinds of initial states.

Measurement-Induced Nonlocality and Geometric Discord in the Spin-Boson Model

Dynamics of measurement-induced-nonlocality (MIN) and geometric measure of discord (GD) in the spin-boson model is studied. Analytical results show that for two large classes of initial states, MINs are equal but GDs are different. At the end of evolution, MIN and GD initially stored in the spin system transfer completely to reservoirs. The quantum beats for MIN and GD are also found which are the results of quantum interference between two local non-Markovian dynamics via quantum correlation.

Monogamy of Measurement-Induced Nonlocality Based on Relative Entropy

In this paper, using relative entropy, we study monogamous properties of measurement-induced nonlocality based on relative entropy. Depending on different measurement sides, we provide necessary and sufficient conditions for two types of monogamy inequalities. By the concept of nonlocality monogamy score, we find a necessary condition of the vanished nonlocality monogamy score for arbitrary three-party states. In addition, two types of necessary and sufficient conditions of the vanished nonlocality monogamy scores are obtained for any pure states. As an application, we show that measurement-induced nonlocality based on relative entropy can be viewed as a "nonlocality witness" to distinguish generalized GHZ states from the generalized W states.

Superactivation of Measurement-Induced Nonlocality

Nonlocality, as an essential, subtle and intriguing aspect of nature, has many different facets and manifestations. In quantum information theory, nonlocality is usually defined, characterized and quantified in the framework of entanglement and violation of certain Bell inequalities. An exciting phenomenon concerning entanglement-related nonlocality is the superactivation, symbolized as " 0 + 0 > 0", which means that two systems, while do not possess nonlocality individually by themselves, may exhibit nonlocality when combined together in an independent fashion. In this work, we explore nonlocality from the measurement perspective and reveal the superactivation of measurement-induced nonlocality(MIN): When two bipartite states with vanishing MIN are combined together, the tensorizing state may possess non-zero MIN. Implications and applications are discussed.

Dynamics of Measurement-Induced Disturbance for a Qubit-Qutrit System in Noninertial Frames

We investigate the dynamics of measurement-induced disturbance(MID) for a qubit-qutrit system in noninertial frames under various multi-local decoherence channels(i.e.,dephasing,phase-flip,bit-(trit-) flip,bit-(trit-) phase-flip,and depolarizing channels).We find that,for any acceleration,the MID can decay in a monotonic way to zero or to a nonzero steady value(i.e.,residual MID exists).Consequently,no sudden death of the MID occurs,which is different from entanglement.

Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field

Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance （MID）. We show that the behaviors of the MID are remarkably different from the con- currence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant Jz, while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter ）,, whereas an opposite effect for MID behaviors is presented.

Correlation dynamics of two-parameter qubit-qutrit states under decoherence

We investigate the dynamics of correlations for two-parameter qubit--qutrit states under various local decoherence channels including depalising, phase-flip, bit- and trit-flip, bit- and trit-phase-flip, and depolarizing channels. We find that, under certain conditions, the classical： correlations may not be affected by the noise or decay monotonically. The quantum correlations measured by measurement-induced disturbance （MID） show three types of dynamical behaviors： （i） monotonic ＇decay to zero, （ii） monotOniC decay to a nonzero steady value, （iii） increase from zero and then decrease to zero in a monotonic way. Consequently, we find that, differing from the dynamics of entanglement, the present classical and quantum correlations do not reveal sudden death behavior.

Property of Quantum Correlations with Correlated Noise

We analyze the classical and quantum correlation properties of the standard and so-called quasiclassical depolarizing channel with correlated noise and non-Markovian dephasing channel, specifically we use the quantum discord, entanglement, and measurement-induced disturbance （MID） to measure the quantum correlations. For the depolarizing channel, we find that the memory effect has more influence on the MID and quantum discord than entanglement. For the dephasing channel, we show that the non-Markovian dephasing channel is more robust than Markovian dephasing channel against deeoherence. We also find that at first MID and quantum discord take different values, and then after a specific time they will take almost the same value and both decay monotonically in the same way.

Correlation dynamics of a qubit qutrit system in a spin-chain environment with Dzyaloshinsky Moriya interaction

We study the dynamics of correlations for a hybrid qubit-qutrit system in an XY spin-chain environment with Dzyaloshinsky-Moriya interaction. Our discussion involves a comparative analysis of negativity, quantum discord, and measurement-induced disturbance. It is found that the quantum discord is optimal of the three quantum correlations to de- tect the critical point of quantum phase transition. Only when the qubit interacts with the environment, is the phenomenon of sudden transition between the classical correlation and the quantum discord observed. Moreover, the Dzyaloshinsky- Moriya interaction enhances the decay of quantum correlations.

A two-dimensional quantum walk driven by a single two-side coin

We study a two-dimensional quantum walk with only one walker alternatively walking along the horizontal and vertical directions driven by a single two-side coin.We find the analytical expressions of the first two moments of the walker’s position distribution in the long-time limit,which indicates that the variance of the position distribution grows quadratically with walking steps,showing a ballistic spreading typically for quantum walks.Besides,we analyze the correlation by calculating the quantum mutual information and the measurement-induced disturbance respectively as the outcome of the walk in one dimension is correlated to the other with the coin as a bridge.It is shown that the quantum correlation between walker spaces increases gradually with the walking steps.

Thermal quantum and total correlations in spin-1 bipartite system

Thermal quantum and total correlations of a two spin-1 Ising model in the presence of an external homogeneous magnetic field and the Dzyaloshinski-Moriya （DM） interaction are investigated. The result indicates that the DM interaction plays a leading role in the quantum correlation measured by measurement-induced disturbance except for the region with small DM interaction and low temperature, while the DM interaction and the external magnetic field play competing roles in the negativity. The thermal total correlations measured by an alternative new measure defined in terms of the Wigner-Yanase skew information and the quantum mutual information display differences in the same region.

Quantum Correlations in Werner Derivatives

Quantum correlations in Werner derivatives are studied with two different approaches, i.e., measurement- induced disturbance （MID） [Phys. Rev. A 77 （2008） 022301] and ameliorated MID （AMID） [J, Phys. A 44 （2011） 352002]. They are derived via strict deductions with MID while numerically calculated via the measurement optimization with AMID. Interestingly, quantum correlations captured with both approaches are completely coincident. Moreover, some distinct features of the quantum correlations and their underlying physics are exposed via analyses and discussions.

Quantum Correlations in a Two-Qubit Heisenberg XX Model under Intrinsic Decoherence

Taking into account the intrinsic decoherence, we have investigated quantum correlations in a two-qubit Heisenberg XX model when a nonuniform magnetic field is included. We compare entanglement measured by entan- glement of formation, quantum discord and measurement-induced measurement （MID） and illustrate their different characteristics. Quantum discord and MID show the same features and always exist even though there is no entangle- ment in the long time limit. In the time evolution, quantum discord could be generated or enhanced to the stable value, while MID just decreases to the stable value.