Chong Li, He-Shan Song, Ling Zhou, Chun-Feng Wu
A new protocol for quantum key distribution based on entanglement swapping is presented. In this protocol, both certain key and random key can be generated without any loss of security. It is this property differs our protocol from the previous ones. The rate of generated key bits per particle is improved which can approach six bits (4 random bits and 2 certain bits) per four particles.
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In a recent paper [J. Opt. B: Quantum Semiclass. Opt. 5 (2003) 155-157], a quantum key distribution scheme based on entanglement swapping was proposed, which exhibited two improvements over the previous protocols. In this Comment, it is shown that the scheme has no properties as been discussed.
The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios
本文证明了排他性基本构件（奇孔和最简单的奇反孔）的量子极大值概率无法在Bell场景中实现，并据此提出推测，同时解释了量子概率判定问题的差异及原理识别的简化。
As shown by Pitowsky, the Bell inequalities are related to certain classes of probabilistic inequalities dealt with by George Boole, back in the 1850s. Here a short presentation of this relationship is given. Consequently, the Bell inequalities can be obtained without any assumptions of physical nature, and merely through mathematical argument.
Catalytic Activation of Bell Nonlocality
通过催化过程，贝尔局部态可被转换为贝尔非局部态，展示了量子催化与贝尔非局域性超激活的新机制。
Without imposing the locality condition,it is shown that quantum mechanics cannot reproduce all the predictions of a special stochastic realistic model used in certain spin-correlation experiments.This shows that the so-called locality condition is an unnecessary assumption of Bell's theorem.
A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.
Here we show that, if we insert context dependent unitary evolutions (which can be achieved via post selection) into spatial (i.e., normal) Bell-CHSH test, then it is possible to violate space-time Bell-CHSH inequality maximally (i.e., up to $4$). However this does not contradict Tsirelson quantum bound ($2\sqrt{2}$), as the latter has been derived without taking into consideration context dependent unitary evolutions and/or post selection. As an important application, this leads to a more efficient quantum key distribution protocol.
It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (``Bell Locality'') and the empirically well-supported predictions of quantum theory for the standard EPR-Bell setup. The demonstrated hidden variables are precisely those needed for the derivation of the Bell Inequalities. We thus refute the widespread view that empirical violations of Bell Inequalities leave open a choice of whether to reject (i) locality or (ii) hidden variables. Both principles are indeed assumed in the derivation of the inequalities, but since, as we demo…
We analyze certain aspects of group theoretical approach to Bell inequalities proposed by Güney and Hillery. The general procedure for constructing the relevant group orbits is described. Using Hall theorem we determine the form of Bell inequality in the single orbit case. It is shown that in this case the Bell inequality is not violated for maximally entangled state generating trivial subrepresentation if the representation under consideration is real.
We generalize Bell's inequalities to biparty systems with continuous quantum variables. This is achieved by introducing the Bell operator in perfect analogy to the usual spin-1/2 systems. It is then demonstrated that two-mode squeezed vacuum states display quantum nonlocality by using the generalized Bell operator. In particular, the original Einstein-Podolsky-Rosen entangled states, which are the limiting case of the two-mode squeezed vacuum states, can maximally violate Bell's inequality due to Clauser, Horne, Shimony and Holt. The experimental aspect of our scheme and nonlocality of arbitra…
An explanation of the Bell experiment
基于量子力学基础的新方法，指出观察者心智的局限性影响贝尔定理，并具有更广泛意义。
For a special stochastic realistic model in certain spin-correlation experiments and without imposing the locality condition, an inequality is found. Then, it is shown that quantum theory is able (is possible) to violate this inequality. This shows that, irrelevance of the locality condition, the quantum entanglement of the spin singlet-state is the reason for the violation of Bell's inequality in Bell's theorem.
The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by Bass and stated in full generality by Vorob'ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objectiv…
What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.
Bell state measurement (BSM) plays a vital role in quantum information. There are many researches on BSM of qubit Bell state, however, there is no definite solution of how to realize high-dimensional Bell state measurement (HDBSM). In this paper, We present a scheme for realizing arbitrary high-dimensional two-particle Bell state measurement by auxiliary entanglement. In our scheme, the maximal entangled states with different degrees of freedom (DOF) are used as auxiliary states, and then the HDBSM can be achieved by implementing Bell measurement with different degrees of freedom. We present t…
Two tripartite schemes are put forward with shared entanglements and LOCC for sharing an operation on a remote target sate. The first scheme uses a Bell and a symmetric W states as quantum channels, while the second replaces the symmetric W state by an asymmetric one. Both schemes are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that, the latter scheme is better than the former one. Particularly, the sharing can be achieved only probabilistically with the first scheme…
Separability and entanglement for n-qubits systems are quantified by using Hilbert-Schmidt (HS) decompositions in which the density matrices are decomposed into various terms representing certain one qubit, two-qubits,and larger qubits measurements. The present method is more general than previous methods for bipartite systems as it can be used for quantification of entanglement for large n-qubits systems.We demonstrate the use of such method by analyzing three qubits GHZ states, and three qubits general Bell states produced by a certain multiplications of Braid operators, operating on the com…
We consider typical experiments that use Bell-inequalities to test local-realist theories of quantum mechanics and gain insight into how certain results can be obtained. We see that results against local-realism arise from some `quantum skew' of the correlation between entangled qubit pairs. Furthermore, we find some conditions necessary for a conclusion against local-realism. Finally we show that the problem of `no-signalling' that arises in these experiments cannot be reduced to arbitrary experimental accuracy.
In a recent paper [arXiv:1703.11003] on this journal Stephen Boughn argued that quantum mechanics does not require nonlocality of any kind and that the common interpretation of Bell theorem as a nonlocality result is based on a misunderstanding. In this note I argue that the Boughn arguments, that summarize views widespread in certain areas of the foundations of quantum mechanics, are based on an incorrect reading of the presuppositions of the EPR argument and the Bell theorem and, as a consequence, are totally unfounded.
There is a direct correspondence between two-particle, entangled quantum states, for example, Bell states, and the relative values of the component one-particle states. This leads to a new rationale for quantum computing which makes use of sequential processing of one-particle states rather than the parallel processing associated with multiparticle states. It is shown that deterministic transformations can correspond to certain Bell state operations. There are some implications for the continuing discussion of quantum realism and entanglement. A principle of relative realism is advocated.
In this paper, the Lorentz transformation of the entangled Bell states with momentum, not necessarily orthogonal to the boost direction, and spin, is studied. We extended quantum correlations and Bell's inequality to the relativistic regime by considering normalized relativistic observables. It is shown that quantum information, along the perpendicular direction to the boost, is eventually lost and Bell's inequality is not always violated for entangled states in special relativity. This could impose restrictions to certain quantum information processing such as quantum cryptography using massi…
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a unique coordination game. In the simplest case, Alice…
We report a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurements. The experimental results demonstrate the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that \emph{all} four Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in pr…
We present a scheme to demonstrate loophole-free Bell inequality violation where the entanglement between photon pairs is transferred to solid state (spin) qubits mediated by cavity QED interactions. As this transfer can be achieved in a heralded way, our scheme is basically insensitive to losses on the channel. This makes it appealing for the implementation of quantum information protocols based on nonlocality, such as device-independent quantum key distribution. We consider potential experimental realisations of our scheme using single atom, colour centre and quantum dot cavity systems.
An efficient and economical scheme is proposed for the perfect quantum teleportation of n-qubit non-maximally entangled state of generalized Bell-type. A Bell state is used as the quantum channel in the proposed scheme. It is also shown that the controlled teleportation of this n-qubit state can be achieved by using a GHZ state or a GHZ-like state as quantum channel. The proposed schemes are economical because for the perfect and controlled teleportation of n-qubit non-maximally entangled state of generalized Bell-type we only need a Bell state and a tripartite entangled state respectively. It…
The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially violate a Bell inequality? Here, we present evidence from two examples. First, we discuss a Bell inequality designed for spin-squeezed states which is violated only by quantum states with a large QFI. Second, we relax a well-known lower bound on the QFI to find the Mermin Bell inequality as a special case. However, a fully general link between QFI and Bell …
Quantum non-locality has been experimentally investigated by testing different forms of Bell's inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constrain on the system's time-correlations. In this paper, we report on the experimental violation of a temporal Bell's inequality using a nitrogen vacancy defect (NV) in diamond and provide a novel quantitative test of quantum coherence. We therefore present a new technique to initialize the electronic state of…
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, which successful implementation is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even nonlocal hidden variable models cannot reproduce the quantum predictions, allows for the device-indep…
A scheme is presented for the dissipative preparation of generalised Bell states of two-qubits, within the context of cavity QED. In the suggested protocol the dissipative processes of spontaneous emission and cavity loss are no longer undesirable, but essential to the required dynamics. Extremely long lived target states are achieved, with fidelities of near unity, utilising cooperativities corresponding to currently available optical cavities. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to cooperativity, such that improved results …
We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single-particle. The spin-{\small 1/2} property of neutrons are utilized. The total wave function of the neutron is described in a tensor product Hilbert space. A Bell-like inequality is derived not by a non-locality but by a contextuality. Joint measurements of the spinor and the path properties lead to the violation of a Bell-like inequality. Manipulation of the wavefunction in one Hilbert…
The connection between quantum optical nonclassicality and the violation of Bell's inequalities is explored. Bell type inequalities for the electromagnetic field are formulated for general states of quantised radiation and their violation is connected to other nonclassical properties of the field. This is achieved by considering states with an arbitrary number of photons and carefully identifying the hermitian operators whose expectation values do not admit any local hidden variable description. We relate the violation of these multi-photon inequalities to properties of phase space distributio…
Quantum correlations, in particular those, which enable to violate a Bell inequality \cite{BELL}, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles $N$. In case of Dicke stat…
Are Bell-tests only about local incompatibility?
本文反驳 Bell 测试仅涉及局域不相容性的观点，指出 Bell-CHSH 不等式违反的关键在于联合测量的非局域不相容性，从而论证非局域性概念不可或缺。
It is shown that no theory that satisfies certain premises can exclude faster-than-light influences. The premises include neither the existence of hidden variables, nor counterfactual definiteness, nor any premise that effectively entails the general existence of outcomes of unperformed local measurements. All the premises are compatible with Copenhagen philosophy, and the principles and predictions of relativistic quantum field theory. The present proof is contrasted with an earlier one with the same objective.
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use entanglement to obtain violations of Bell's inequalities. Even leading and outstanding physicists -- as certainly is the case of Prof. Eberly -- sometimes make elementary mistakes, and this by no means diminishes the importance of their scientific contribution. In general, this is a consequence of an excessive attachment to an idea (nowadays it has become fashiona…
Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell's famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell's inequality. The alternative proofs of Bell's theorem without using Bell's inequality are known as `nonlocality without inequality (NLWI)' proofs. We, review one such proof, namely the Hardy's proof which due to its simplicity and generality has been considered the best version of Bell's theorem.
Certification of quantum correlations and DIQKD at arbitrary distances through routed Bell tests
本文研究路由贝尔实验，证明仅含纠缠量子比特的路由贝尔测试在信道存在任意损耗时仍能认证量子关联，并基于自测试与量子导引概念提出原则上在任意距离下安全的DIQKD协议。
Bell non-locality represents one of the most striking departures of quantum mechanics from classical physics. It shows that correlations between space-like separated systems allowed by quantum mechanics are stronger than those present in any classical theory. In a recent work [Sci. Adv. 7, eabc3847 (2021)], a family of Bell functionals tailored to mutually unbiased bases (MUBs) is proposed. For these functionals, the maximal quantum violation is achieved if the two measurements performed by one of the parties are constructed out of MUBs of a fixed dimension. Here, we generalize this constructi…
Generation of bipartite mechanical cat state by performing projective Bell state measurement
提出利用投影贝尔态测量实现纠缠交换，生成四种二分体声子贝尔猫态，并基于CHSH不等式进行贝尔不等式测试，为连续变量量子网络处理器提供新方法。
According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual 'violation' of Bell inequality to a 'non-violation' for times larger than a characteristic time scale which…
The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning that quantum mechanics can outperform classical physics at tasks associated with such Bell inequalities. Interestingly, however, there exist situations in which this is not the case. We associate an intriguing class of bound entangled states, constructed from unextendable product bases (UPBs) with a wide family of tasks, for which (i) quantum correlations do no…
We construct a space of ideal elements (particles and their paths) to analyze certain aspects of quantum physics. The particles are taken from a model of particle interaction first described by David Deutsch (based on a different but related framework, that of MWI), and the paths are based on Richard Feynman's path-integral formulation of quantum mechanics. By combining the two systems we develop a new approach to quantum mechanics that eliminates various quantum paradoxes.
Quantum Mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and interpretation. Herein, we analyze carefully the possible mathematical meanings of those terms used in analysis of EPR's contention, that Quantum Mechanics is incomplete, as well as Bell's work descendant therefrom. As a result, many inconsistencies and errors in contemporary discussions of nonlocality, as well as in Bell's Ansatz with respect to the laws of probabi…
We present a generalized tomographic quantum key distribution protocol in which the two parties share a Bell diagonal mixed state of two qubits. We show that if an eavesdropper performs a coherent measurement on many quantum ancilla states simultaneously, classical methods of secure key distillation are less effective than quantum entanglement distillation protocols. We also show that certain Bell diagonal states are resistant to any attempt of incoherent eavesdropping.
We investigate theoretically the conditions under which a multi-mode nanomechanical resonator, operated as a purely mechanical parametric oscillator, can be driven into highly nonclassical states. We find that when the device can be cooled to near its ground state, and certain mode matching conditions are satisfied, it is possible to prepare distinct resonator modes in quantum entangled states that violate Bell inequalities with homodyne quadrature measurements. We analyze the parameter regimes for such Bell inequality violations, and while experimentally challenging, we believe that the reali…
Experiments motivated by Bell's theorem have led some physicists to conclude that quantum theory is nonlocal. However, the theoretical basis for such claims is usually taken to be Bell's Theorem, which shows only that if certain predictions of quantum theory are correct, and a strong hidden-variable assumption is valid, then a certain locality condition must fail. This locality condition expresses the idea that what an experimenter freely chooses to measure in one spacetime region can have no effect of any kind in a second region situated spacelike relative to the first. The experimental resul…
Bell pair extraction using graph foliage techniques
本文通过推广图叶状划分技术，为贝尔顶点子式问题提供新工具，并据此给出线图、树图和环图上该问题的精确解。
Steady-state Bell nonlocality in an autonomous quantum thermal machine
研究一种自主量子热机，通过强对称性产生稳态贝尔非局域性，并分析实验缺陷下集体噪声对贝尔非局域性的增强作用。
We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistic…
Trading symmetry for Hilbert-space dimension in Bell-inequality violation
研究对称性在贝尔不等式最大违反中的作用，发现某些对称贝尔不等式需非对称量子策略才能达到最大违反，而对称策略仅能次优。
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum cryptography and tomography or self-testing. Building upon a series of recent works on the geometry of quantum correlations, we are interested in the problem of computing quantum Bell inequalities or the boundary between quantum and post-quantum world. Better knowledge of this boundary will lead to more efficient device-independent quantum processing protocols. We …
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or "loopholes" in available experiment tests, local realist theorie…
Enhancing Microwave-Optical Bell Pairs Generation for Quantum Transduction Using Kerr Nonlinearity
本文提出一种利用微波模式强Kerr非线性的脉冲SPDC方案，通过脉冲驱动产生单光子对，有效缓解了传统方案中保真度与概率的权衡，在有限非线性和光子损失下实现高保真度Bell对的高概率生成。
In contrast to conventional, dynamical entanglement, in which particles with definite identity have uncertain properties, in so-called statistical entanglement, which arises between indistinguishable particles because of quantum symmetry rules, even particle identities are uncertain. The Bell and Kochen-Specker theorems imply that quantum properties either lack realism or possess it with a caveat of contextuality or nonlocality. In the matter of identity of multi-particle states of indistinguishable particles, these contrasting ontological attitudes are mirrored by the "bundle" vs. haecceity v…
We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $ξ$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Bu…
An elegant proof of self-testing for multipartite Bell inequalities
本工作提出了一种简单且广泛适用的自测试论证，用于N体关联贝尔不等式，推广了Mayer-Yao公式并突破了线性不等式限制，为MABK、WWWŻB和Uffink不等式族提供了自测试证明。
We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction is deteriorated in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing the velocity of the observers if the directions of the measurement are fixed. However, this does not imply a…
Consequences of the single-pair measurement of the Bell parameter
本文分析基于弱相互作用测量从单个纠缠对估计整个Bell-CHSH参数的实验结果，探讨其对贝尔不等式检验及量子力学诠释争论的影响。
One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an intermediate step, the development of efficiently computable bounds has played an important role for the advance of the field. In this thesis we phrase the problem of determining the quantum value of a Bell expression in the framework of computational complexity. Then we present our contributions exploring efficiently computable bounds (based on the spectra…
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