Entanglement dynamics and Bell violation of three-qubit states coupled to an XY spin chain with Dzyaloshinski–Moriya interaction

We investigate the entanglement dynamics and Bell violation of three-qubit quantum states under an environment consisting of an XY spin chain with Dzyaloshinski–Moriya (DM) interaction. From the results, we find that the entanglement dynamics depends not only on the DM interaction, the magnetic field, and the anisotropy parameter but also on the number of the freedom degrees of the environment. The decoherence-free subspaces of our model have been identified and the Bell violation of quantum states is also discussed.     

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis-Cummings Model with Phase Decoherence

Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.     

内禀退相干下Tavis-Cummings模型中原子的纠缠演化与贝尔不等式破坏

通过求解系统的Milburn方程，研究了两个二能级原子和单模场相互作用系统中原子间纠缠和贝尔不等式破坏随时间的演化特性，讨论了偶极相互作用、场与原子的失谐量对纠缠度以及贝尔不等式破坏的影响.结果表明：原子间偶极-偶极相互作用对纠缠度和贝尔不等式破坏有显著影响，失谐量增大会使两原子的纠缠度和贝尔不等式破坏变大，并且两原子所能达到稳定的纠缠受偶极相互作用系数与失谐量两者之差的影响.同时还发现两原子的纠缠与贝尔不等式破坏并不是单调的函数关系，很小的纠缠也可以产生贝尔不等式破坏. 关键词： Milburn理论 偶极-偶极相互作用 失谐量 贝尔不等式破坏     

Bell violation for the thermal states of an XXZ spin chain with Dzialoshiski-Moriya interaction

The effect of Dzialoshiski-Moriya (DM) interaction on the violation of Bell inequality for thermal states of interacting qubits via a two-qubit XXZ spin chain is investigated.Our results imply that the DM interaction and anisotropy taking a large positive value can enhance the Bell violation and improve the threshold temperatures of it.By the comparison between the Bell violation and thermal entanglement,we find that the threshold temperatures of thermal entanglement are higher than those of the Bell violation.This implies that some states are entangled but the Bell inequality is not violated.     

The Essence of More Nonlocality with Less Entanglement in Bell Tests

In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more nonlocality with less entanglement. We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane. This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state. But the maximal Bell violation may not always happen on nonmaximally entangled state, because these probabilities will compete with each other, and the Bell violation behaves differently for various CH-type inequalities.     

Is Nonlocality Responsible for the Violation of Bell’s Inequalities?

Bell’s theorem has been widely argued to show that some of the predictions of quantum mechanics which are obtained by applying the Born’s rule to a class of entangled states, are not compatible with any local-causal statistical model, via the violation of Bell’s inequalities. On the other hand, in the previous works, we have shown that quantum dynamics and kinematics are emergent from a statistical model that is singled out uniquely by the principle of Locality. Here we shall show that the local-causal model supports entangled states and give the statistical origin of their generation. We then study the Stern-Gerlach experiment to show that the Born’s rule can also be derived as a mathematical theorem in the local-causal model. These results lead us to argue that nonlocality is not responsible for the quantum mechanical and most importantly experimental violation of Bell’s inequalities. The source(s) of violation has to be sought somewhere else.     

The relation between Hardy’s non-locality and violation of Bell inequality

We give an analytic quantitative relation between Hardy’s non-locality and Bell operator. We find that Hardy’s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy’s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy’s non-locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the Cabello’s argument of Hardy’s non-locality (a generalization of Hardy’s argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy’s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy’s non-locality and Bell operator.     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Direct measurement of decoherence for entanglement between a photon and stored atomic excitation

Violations of a Bell inequality are reported for an experiment where one of two entangled qubits is stored in a collective atomic memory for a user-defined time delay. The atomic qubit is found to preserve the violation of a Bell inequality for storage times up to 21 micros, 700 times longer than the duration of the excitation pulse that creates the entanglement. To address the question of the security of entanglement-based cryptography implemented with this system, an investigation of the Bell violation as a function of the cross correlation between the generated nonclassical fields is reported, with saturation of the violation close to the maximum value allowed by quantum mechanics.     

Entanglement versus bell violations and their behavior under local filtering operations

We discuss the relations between the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity, and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.     

Correlation complementarity yields bell monogamy relations

We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.     

Towards Loophole-Free Optical Bell Test of CHSH Inequality

Bell test had been suggested to end the long-standing debate on the EPR paradox, while the imperfections of experimental devices induce some loopholes in Bell test experiments and hence the assumption of local reality by EPR cannot be excluded with current experimental results. In optical Bell test experiments, the locality loophole can be closed easily, while the attempt of closing detection loophole requires very high efficiency of single photon detectors. Previous studies showed that the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with maximally entangled states requires the detection efficiency to be higher than 82.8 %. In this paper, we raise a modified CHSH inequality that covers all measurement events including the efficient and inefficient detections in the Bell test and prove that all local hidden models can be excluded when the inequality is violated. We find that, when non-maximally entangled states are applied to the Bell test, the lowest detection efficiency for violation of the present inequality is 66.7 %. This makes it feasible to close the detection loophole and the locality loophole simultaneously in optical Bell test of CHSH inequality.     

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.     

Characterization of a two-transmon processor with individual single-shot qubit readout

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own nondestructive single-shot readout. The fixed capacitive coupling yields the sqrt[iSWAP] two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%.     

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.     

Large Violation of Bell Inequalities with Low Entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order \({\frac{\sqrt{n}}{\log n}}\) with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.     

Analysis of elliptically polarized maximally entangled states for bell inequality tests

When elliptically polarized maximally entangled states are considered, i.e., states having a non random phase factor between the two bipartite polarization components, the standard settings used for optimal violation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to compensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensator. This device is employed to correct the phase that appears in the maximally entangled state generated from a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.     

Entanglement Measure and Quantum Violation of Bell-Type Inequality

By calculating entanglement measures and quantum violation of Bell-type inequality, we reveal the relationship between entanglement measure and the amount of quantum violation for a family of four-qubit entangled states. It has been demonstrated that the Bell-type inequality is completely violated by these four-qubit entangled states. The plot of entanglement measure as a function of the expectation value of Bell operator shows that entanglement measure first decreases and then increases smoothly with increasing quantum violation.