Sharing quantum nonlocality in star network scenarios

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.     

Comment on “the rastall model and Stapp's proof of nonlocality”

It is shown that the argument set forth as being my argument is fundamentally different from my argument.1. This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.     

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.     

Effects of photon addition on quantum nonlocality of squeezed entangled coherent states

Effects of photon addition on quantum nonlocality of squeezed entangled coherent states for Bell-inequality tests are studied theoretically. By utilizing the method of photon-parity measurement, it is found that photon addition can always increase the degrees of Bell violations within a certain parameter range. A possible scheme for generating photon-added squeezed entangled coherent states is proposed.     

Effects of photon addition on the quantum nonlocality of squeezed entangled-coherent states

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states for Bell-inequality tests are studied theoretically. By utilizing the method of photon-parity measurement, it is found that photon addition can always increase the degrees of Bell violations within a certain parameter range. A possible scheme for generating photon-added squeezed entangled coherent states is proposed.     

Comments on “determinism,realism, and Stapp's 1985 proof of nonlocality”

An earlier argument by the author, that Stapp's 1985 proof of quantum locality contains an implicit element of realism, is elaborated. Refuted thereby is Clifton's criticism that the author's argument was based on a misinterpretation of counterfactual analysis.     

Determinism,realism, and Stapp's 1985 proof of nonlocality

Two recent criticisms of Stapp's 1985 proof of an incompatibility between locality and quantum mechanics are clarified. One of these criticisms (charging that the proof requires determinism) is supported by a detailed logical analysis of the locality conditions in the proof. The other criticism (charging that the proof assumes realism) is shown to be based upon a misinterpretation of the rôle of counterfactuals in the proof. Further, Stapp's own replies to these criticisms are shown to be inadequate.     

广义GHZ态的纠缠与非定域性

对GHZ态与W态叠加的三粒子广义GHZ态,用Svetlichny不等式,给出了其非定域性的解析表达式.用数值计算方法讨论了纠缠与非定域性之间的关系. 关键词： 广义GHZ态 剩余纠缠 Svetlichny不等式 非定域性     

Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.      

Nature of Nonlocality in Triangle Network based on Elegant Joint Measurement

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.     

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.     

Quantum nonlocality for two-mode correlated states based on generalized pseudospin operators

In this Letter, we investigate the quantum nonlocality of two-mode correlated states. We find that the pseudospin formalism [Z.B. Chen, J.W. Pan, G. Hou, Y.D. Zhang, Phys. Rev. Lett. 88 (2002) 040406] generally fails to depict the nonlocality of the states when the photon number difference between the two modes is odd. The formalism is then generalized such that the nonlocality of a two-mode correlated state can be well revealed without regard to the difference. Later we consider the nonlocality of the two-mode intelligent SU(1,1) states in the generalized formalism and compare our results with the entanglement of the corresponding states.     

Uncertainty-induced quantum nonlocality

Based on the skew information, we present a quantity, uncertainty-induced quantum nonlocality (UIN) to measure the quantum correlation. It can be considered as the updated version of the original measurement-induced nonlocality (MIN) preserving the good computability but eliminating the non-contractivity problem. For 2×d$2\times d$-dimensional state, it is shown that UIN can be given by a closed form. In addition, we also investigate the maximal uncertainty-induced nonlocality.     

等距离耦合腔系统中的非局域性

本文研究的物理系统由3个二能级原子和3个等距离单模腔构成. 3个单模腔分别处于等边三角形的3个顶点, 腔与腔之间通过光纤耦合. 采用Mermin-Ardehali-Belinksii-Klyshko不等式(简称MABK不等式)表征三体量子态的非局域性. 本文利用数值计算方法, 研究了原子初态或腔场初态为W态情况下三体系统量子态的MABK不等式违背, 讨论了腔模与光纤模间的耦合系数变化对MABK不等式违背的影响. 计算结果表明: 三原子量子态和三腔场量子态均呈现出MABK不等式违背, 并且随腔模与光纤模间耦合系数增大, 三原子量子态的非局域性增强.     

The rastall model and Stapp's proof of nonlocality

Recently two distinct arguments have been given (by Stapp, and Bedford and Stapp) to prove that a model proposed by Rastall for the statistics of EPR-correlated spin-1/2 particles, which happens to violate the Bell inequality, conflicts with locality. Neither argument makes use of the fact that the Rastall model violates the Bell inequality; therefore both seem to provide independent support for a more general proof of Stapp's, which allegedly establishes that any model violating this inequality, including quantum mechanics, must imply the existence of nonlocal influences. However, it is shown here that both of these arguments are invalid under an indeterministic interpretation of quantum mechanics, a conclusion which agrees with the same criticism made by other authors but directed against Stapp's more general proof of nonlocality.2. For a clarification and defence of Kraus' claim, see the discussion of the broken square problem in [7], Sec. 2.1.3. These strict [anti-] correlations do not rigorously exclude the possibility that the L and R meterscould register +1, –1 [+1, +1] or –1, +1 [–1, –1] for any pair in the measured sample; by the law of large numbers, they only render these possibilities highly improbable. However, I shall follow Rastall, Bedford and Stapp in regarding such possibilities as strictly impossible (cf. also Note 9).4. Eberhard, himself, uses his discovery that matching is sufficient for BI to attempt a proof, in the style of Stapp [1], that BILOC.5. A world or state of affairs is properly specified only after a list of the truth values forall of the propositions describingall of the events which occur in that world is provided. Since there exist various possible permutations of these truth values, we must hypothetically consider, for instance in the first part of this example, the two (in general, uncountably infinite)classes of worlds: those with the meters set to measurea andc and those with the meters set toa andd. Each class can be further divided into subclasses according to the values that the various responses take on in each world. The idea that a counterfactual supposition leads to a class of worldssufficiently similar (by some standard of similarity) to the actual world is exploited in Lewis' [13] semantics for counterfactuals; but I shall not need to adopt any particular semantics of counterfactuals here beyond using some standard valid inferences involving them.6. To be fully rigorous, this demand should be broken down into: (a) supposing that RM is true at the actual world; and (b) demanding that the truth of physical laws as depicted by RM be independent of whether or not measurements are undertaken. For a more thorough discussion, see the justification of the principle CUW in [7].7. Kraus [14] objects to Stapp's argument on the grounds that it invokes concepts without direct observational meaning. But presumably then he would rejectany use of counterfactuals (including their use in Stapp's more general proof) on the same grounds. Also, it is worth adding (to Stapp's [5] own reply to Kraus) that Kraus' additional charge that Stapp's argument is suspect because it uses the language of things waiting to be measured if and when the appropriate instrument is applied misinterprets Stapp's [6] use of the word thing. For this word is used in a sense equivalent to what I have called response; and, by definition, responses are (in general, counterfactually)measured values having nothing to do with entities apart from measurement.8. Although these authors choose Lewis' semantics for analyzing counterfactuals (cf. Note 5) in their critiques, their arguments do not turn upon this choice but are motivated on physical grounds. For the same critique without the Lewis framework see [18] and my (slightly different) argument in the text.9. Strictly speaking, since improbability does not imply impossibility (cf. Note 3), the conditionals in the RM premisses of Parts 1 and 2 must also be weakened to conditionals, which weakens C1 and C2 in the same way, and hencealso undermines Stapp's argument.10. Towards the end of their paper, BS restate UR in a way that lends it easily to confusion with the stronger statement for every measurementM, there exists a particular measurement resultx, such that anM measurementwould yieldx (cf. [7] for a discussion of further instances where this confusion has occurred). Sincex = +1 or –1, this statement implies that every measurement eitherwould yield +1or would yield –1, which (as we have seen) implies determinism. (The difference between this statement and the weaker (uncontroversial) UR I adopt in the text is that the former can be obtained from the latter by distributing the would over the disjunction or.) If UR were interpreted in this stronger sense, so as to make it imply determinism (rather than just determinateness of responses in each world), then the Stapp and BS proofs could go through; although, obviously, UR would then have to be rejected by the indeterminist.     

Acceleration‐induced nonlocality: kinetic memory versus dynamic memory

The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. We show that only kinetic memory is acceptable, since dynamic memory leads to divergences for nonuniform accelerated motion.     

Reply to “quantum nonlocality without counterfactual definiteness?”

It is shown why the objections raised do not pertain to my proof.     

Necessity of acceleration‐induced nonlocality

The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. This locality postulate is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties in general cannot be measured instantaneously. The problem is corrected in nonlocal relativity by supplementing the locality postulate with a certain average over the past world line of the observer.     

Observers in spacetime and nonlocality

Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr‐Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers must be nonlocal. Nonlocal electrodynamics of non‐uniformly rotating observers is discussed and the consequences of this theory for the phenomenon of spin‐rotation coupling are briefly explored.