The Present Situation in Quantum Theory and its Merging with General Relativity

We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.)     

通过设计量子库来调控量子比特间的Bell非定域性研究

量子系统间的Bell非定域性是一种比量子纠缠更为严格的量子关联,它在刻画多体量子关联有着不可或缺的作用.类似于量子纠缠,在开放两量子比特和三量子比特系统中的Bell非定域性可能会出现猝死现象.本文建议了一个可供选择的方案即在热库环境中通过增加辅助粒子来调控两量子比特和三量子比特间的Bell非定域性动力学.研究发现：通过调节辅助粒子数目,不仅两量子比特和三量子比特系统的Bell非定域性可以避免猝死现象的发生,而且在长时间极限下它能维持在一个较高水平.论文得到的结果将对多体量子系统间量子关联的调控和避免猝死现象等相关研究有积极的指导意义.     

The Quantum World is not Built up from Correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The Bell inequality argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.     

Chain Inequality Violation with Quantum Weak Measurement Technology

Bell inequality is an important resource in the quantum information theory, which can be applied to guarantee security of the device independent quantum information protocols. By utilizing the quantum weak measurement technology, we propose the Chain inequality violation with three parties, and the analysis result demonstrates that double Chain inequality violation can be observed in the case of Alice and Bob have two different measurement bases.Since the weak measurement model can be assumed to be an eavesdropping model, our analysis model may be applied to analyze security of the device independent quantum information protocols.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.     

Application of the 1H(d,2He)n reaction to the EPR paradox

The test of the local hidden variable theories involving strongly interacting pairs of massive spin- $\frac{1}{2}$ hadrons, in a nearly loophole-free experimental setting is reported. The spin correlation function is deduced to be C _exp(π/4) = ?0.73 ± 0.08. This result is in agreement with non-local quantum mechanical prediction and it violates the Bell’s inequality of C _Bell(π/4) ≥ ?0.5 at a confidence level of 99.3%.     

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.     

Reassessment of Leggett Inequality

Leggett formulated an inequality that seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that the theory applies to a class of local theory. Contrary to what happens in the derivation of Bell inequality, it is not necessary to make the hypothesis of outcome independence to derive the Leggett inequality.     

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.     

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.     

No signaling and quantum key distribution

Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct. It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles. The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely. Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling. Its security stems from violation of a Bell inequality.     

Quantum Information in Relativity: The Challenge of QFT Measurements

Proposed quantum experiments in deep space will be able to explore quantum information issues in regimes where relativistic effects are important. In this essay, we argue that a proper extension of quantum information theory into the relativistic domain requires the expression of all informational notions in terms of quantum field theoretic (QFT) concepts. This task requires a working and practicable theory of QFT measurements. We present the foundational problems in constructing such a theory, especially in relation to longstanding causality and locality issues in the foundations of QFT. Finally, we present the ongoing Quantum Temporal Probabilities program for constructing a measurement theory that (i) works, in principle, for any QFT, (ii) allows for a first- principles investigation of all relevant issues of causality and locality, and (iii) it can be directly applied to experiments of current interest.     

On the consequences of Einstein locality

After some considerations about the equivalence of the objective local theories to the deterministic theories of Bell's type, a simple and systematic way to deduce inequalities from Einstein locality is introduced: All the inequalities deduced by Bell and by other authors, as well as several new ones, are so obtained. Some theorems are proven which show how striking the difference is at small angles between a correlation function satisfying Einstein locality and the quantum mechanical one. Experiments at small angles involve weaker additional assumptions than those used up to now in experimental research on Bell's inequality.     

The Modified Bell Inequality and Its Physical Implications in the ESR Model

The extended semantic realism (ESR) model proposes a theoretical perspective which reinterprets quantum probabilities as conditional on detection rather than absolute and embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual, hence local, framework. The assumptions needed to prove the Bell inequality therefore hold in the ESR model, but we show that the Bell inequality must be substituted in it by the modified Bell inequality and that the standard quantum expectation values, when reinterpreted as proposed by the ESR model, do not violate the latter inequality. Hence the long-standing conflict between ??local realism?? and QM is settled in the ESR model. Finally we provide an elementary example of a prediction that might be used to check whether the ESR model is correct.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.     

Manifestly Covariant Quantum Theory with Invariant Evolution Parameter in Relativistic Dynamics

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard Model. The anomalies include neutrino oscillations, non-locality, and gravity.     

Fine-grained uncertainty relation for open quantum system

The fine-grained uncertainty relation(FUR) is investigated for accelerating open quantum system, which manifests the celebrated Unruh effect, a crucial piece of the jigsaw for combining relativity and quantum physics. For a single detector, we show that the inevitable Unruh decoherence can induce a smaller FUR uncertainty bound, which indicates an additional measurement uncertainty may exist. For an open system combined with two detectors, via a nonlocal retrieval game, the related FUR uncertainty bound is determined by the non-classical correlation of the system. By estimating the maximal violation of Bell inequality for an accelerating system, we show that the FUR uncertainty bound can be protected from Unruh decoherence, due to quantum correlation generated through Markovian dynamics.     

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.