Measurement-induced disturbance and thermal negativity of qutrit-qubit mixed spin chain

We investigate the quantum correlation in a qutrit-qubit mixed spin chain based on measurement-induced disturbance (MID) [S. Luo, Phys. Rev. A, 77 (2008) 022301]. We also compare MID and thermal entanglement measured by negativity and illustrate their different characteristics.     

Polarization correlation in the two-photon decay of atomic hydrogen: nonlocality versus entanglement

From the work by Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], photon pairs from the 2s _1/2 → 1s _1/2 (two-photon) decay of atomic hydrogen are known to be quantum mechanically correlated. In these experiments, the polarization states of the photons emitted in back-to-back geometry were shown to violate the Bell inequality as a qualitative sign of nonlocality and entanglement. In the present contribution, we analyze how these nonlocal quantum correlations, as given by the violation of the Bell inequality, differ from the concurrence as a true entanglement measure. Results are shown for both quantifiers in dependence of the decay geometry and the initial polarization of the atoms for the 2s _1/2 → 1s _1/2 and 3d _5/2 → 1s _1/2 two-photon decay of atomic hydrogen. These results display the difference between nonlocality and entanglement and, hence, may stimulate further experiments on nonlocal quantum correlations in atomic systems.     

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four different approaches, namely, quantum discord [Phys. Rev. Lett. 88 (2002) 017901], measurement- induced disturbance (MID) [Phys. Rev. A 77 (2008) 022301], ameliorated MID [J. Phys. A: Math. Theor. 44 (2011) 352002] and quantum dissonance [Phys. Rev. Lett. 104 (2010) 080501]. Quantum correlations captured with different approaches are compared and discussed so that their three distinct features are exposed.     

Measurement-induced nonlocality

We interpret the maximum global effect caused by locally invariant measurements as measurement-induced nonlocality, which is in some sense dual to the geometric measure of quantum discord [Dakic, Vedral, and Brukner, Phys. Rev. Lett. 105, 190502 (2010)]. We quantify measurement-induced nonlocality from a geometric perspective in terms of measurements, and obtain analytical formulas for any dimensional pure states and 2 × n dimensional mixed states. We further derive a tight upper bound to measurement-induced nonlocality in general case. The physical significance of measurement-induced nonlocality is discussed in the context of correlations, entanglement, quantumness, and cryptographic communication.     

Experimental investigation of tripartite entanglement and nonlocality in three-qubit generalized Greenberger–Horne–Zeilinger states

We investigate theoretically and experimentally the tripartite entanglement defined by V. Coffman [Phys. Rev. A 61 (2000) 052306] and nonlocality expressed by the Mermin inequality [Phys. Rev. Lett. 65 (1990) 1838] in three-qubit generalized Greenberger–Horne–Zeilinger (GGHZ) states. Using our GGHZ states with fidelity ∼0.84, we demonstrate experimentally the theoretical results of tripartite entanglement and the Mermin theorem successfully. It is shown that the experimental results are in good agreement with the theoretical predictions.     

Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.     

Quantum Correlations in a Family of Two-Qubit Separable States

Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four diferent approaches,namely,quantum discord[Phys.Rev.Lett.88(2002)017901],measurementinduced disturbance(MID)[Phys.Rev.A 77(2008)022301],ameliorated MID[J.Phys.A:Math.Theor.44(2011)352002]and quantum dissonance[Phys.Rev.Lett.104(2010)080501].Quantum correlations captured with diferent approaches are compared and discussed so that their three distinct features are exposed.     

Quantum nonlocality and partial transposition for continuous-variable systems

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.     

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 non-Markovian environments

We have studied the analytical Markovian and non-Markovian dynamics of quantum correlations, such as entanglement, quantum discord and Bell nonlocalities for three noisy qubits. Quantum correlation as measured by quantum discord is found to be immune to death contrary to entanglement and Bell nonlocality for initial GHZ- or W-type mixed states.     

Geometric measure of quantum discord over two-sided projective measurements

The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlations more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502] introduced a geometric measure of quantum discord, Luo and Fu [Phys. Rev. A 82 (2010) 034302] simplified the variation expression of this geometric measure. In this Letter we introduce a geometric measure of quantum discord over two-sided projective measurements. A simplified expression and a lower bound of this two-sided geometric measure are derived and explicit expressions are obtained for some special cases.     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665] .In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.     

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys.Rev.Left.71 (1993) 1665].In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field.Then state-selective measurements are performed on these atoms,which may reveal quantum nonlocality without using Bell inequality.We also propose a simple scheme for the generation of multi-atom entangled states.``     

Measurement-induced disturbance and thermal entanglement in spin models

Quantum correlation in two-qubit spin models is investigated by use of measurement-induced disturbance [S. Luo, Phys. Rev. A, 77 (2008) 022301]. Its dependences on external magnetic field, spin–spin coupling, and Dzyaloshinski–Moriya (DM) interactions are presented in detail. We also compare measurement-induced disturbance and thermal entanglement in spin models and illustrate their different characteristics.     

Entanglement and nonlocality in multi-particle systems

Entanglement, the Einstein–Podolsky–Rosen (EPR) paradox and Bell’s failure of local-hiddenvariable (LHV) theories are three historically famous forms of “quantum nonlocality”. We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose–Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger–Horne–Zeilinger (GHZ) states, and the ground state of a two-well BEC.     

Continuous Variable Entanglement and Violation of Bell Inequality for Two Modes in a Three-Level Cascade Atomic System

Continuous variable entanglement and violation of Bell inequality for two modes are investigated in a three-level cascade atomic system. Entanglement of the system is demonstrated according to the entanglement criterion [Phys. Rev. Lett. 84 （2000）2722]. Violation of Bell inequality is studied within the framework of a quantum theory of multiwave mixing. It is shown that there are some states that are entangled but do not violate the Bell inequality.     

Output nonlocality and nonclassicality in a two-mode entanglement laser

Output nonlocality and nonclassicality for the two modes are investigated in an entanglement laser sys-tem. Within the framework of a quantum theory of multiwave mixing,nonlocality and nonclassicality are discussed according to the violations of Bell inequality and Cauchy-Schwarz inequality. It is found that both nonlocality and nonclassicality can be fulfilled in the outside cavity fields under certain conditions. It is also shown that there are some nonclassical states that do not show nonlocality.     

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.     

Nonlocality in many-body quantum systems detected with two-body correlators

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.     

Quantum Correlations in Werner Derivatives

Quantum correlations in Werner derivatives are studied with two diferent approaches,i.e.,measurementinduced 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.