Helmut Dersch
Local systems may appear to violate Bell's inequalities if they are observed through suitable filters. The nonlocality leading to violation is outside the system and comprises the observer comparing the outcomes of the typical two wing Bell experiment. An example based on a well known gedanken experiment by Mermin is presented, and implications for the interpretation of Bell tests are discussed.
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It is shown that Marinatto's claim [Phys. Rev. Lett. 90, 258901 (2003)] that the proof of "Bell's theorem without inequalities and without probabilities for two observers" [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] requires four spacelike separated observers rather than two is unjustified.
A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.
A derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and three possible local settings. The procedure can be extended straightforwardly to multiparty correlations.
We show that it is possible to have arbitrarily long sequences of Alices and Bobs so every (Alice, Bob) pair violates a Bell inequality. We propose an experiment to observe this effect with two Alices and two Bobs.
Bipartite Bell inequalities can be simultaneously violated by two different pairs of observers when weak measurements and signaling is employed. Here we experimentally demonstrate the violation of two simultaneous CHSH inequalities by exploiting a two-photon polarization maximally entangled state. Our results demonstrate that large double violation is experimentally achievable. Our demonstration may have impact for Quantum Key Distribution or certification of Quantum Random Number generators based on weak measurements.
A proof of Bell's theorem using two maximally entangled states of two qubits is presented. It exhibits a similar logical structure to Hardy's argument of ``nonlocality without inequalities''. However, it works for 100% of the runs of a certain experiment. Therefore, it can also be viewed as a Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated regions.
Here we present a Multiple Observer Probability Analysis (MOPA) for the purpose of clarifying topics in experimental Bell scenarios. Because Bell scenarios are interested in quantum effects between nonlocal measurement devices, we assign an observer to each device: Alice and Bob. Given that the observers are stationary and space-like separated, each observer is privy to different information along their shared equi-temporal lines due to permutations in the order they observe events. Therefore, each observer is inclined to assign different probability distributions to the same set of propositio…
Sharing preparation contextuality in Bell experiment by arbitrary pair of sequential observers
针对含 $n$ 与 $2^{n-1}$ 次测量的双粒子 Bell 不等式，本文证明非定域性仅能由首对顺序观测者共享，而制备语境性可由任意一对独立顺序观测者共享。
Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a counterexample, which will be presented soon. Thus our thesis is dead. Still the series of Bell inequalities discussed in the manuscript (v1) form a necessary condition for local realism, and are tight. They are tight and complete (sufficient) only for N=3 settings per observer (as shown in quant-ph/0611086, fortunately using an entirely different approach).
In this Comment we show that Cabello's argument [Phys. Rev. Lett. 86, 1911 (2001)] which proves the nonlocal feature of any classical model of quantum mechanics based on Einstein-Podolsky-Rosen (EPR) criterion of elements of reality, must involve at least four distant observers rather than the two employed by the author. Moreover we raise a remark on the necessity of performing a real experiment confirming Cabello's argument.
Past, present and future experimental tests of quantum nonlocality are discussed. Consequences of assuming that the state-vector collapse is a real physical phenomenon in space-time are developed. These lead to experiments feasible with today's technology.
There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L…
We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)] to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell's inequality which resembles Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)] but requires only two observers.
We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes of states for which all standard Bell's inequalities with two measurement settings per observer are satisfied.
We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer.
This paper describes a device, consisting of a central source and two widely separated detectors with six switch settings each, that provides a simple gedanken demonstration of Bell's theorem without relying on either statistical effects or the occurrence of rare events. The mechanism underlying the operation of the device is revealed for readers with a knowledge of quantum mechanics.
Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the nonlocality present in a single particle from an entangled pair using the method of weak measurements [Phys. Rev. Lett. {\bf 114}, 250401 (2015)]. Here we report an observation of double CHSH…
Decoherence is an unavoidable phenomenon that results from the interaction of the system with its surroundings. The study of decoherence due to the relativistic effects has the fundamental importance. The Unruh effect is observed by the relativistically accelerator observer. The unruh effect acts as a quantum channel and we call it the Unruh Channel. The Unruh channel can be characterize by providing its Kraus representation. We consider the bipartite scheme in which the quantum information is shared between an inertial observer (Alice) and an accelerated observer (Rob) in the case of Dirac fi…
Unmasking the Polygamous Nature of Quantum Nonlocality
该研究打破了Bell违反单偶性的普遍认知，证明量子非定域性具有多偶性，提出了识别多偶情形的系统方法，并通过六光子Dicke态实验验证，成果可用于多方量子密钥分发与量子网络多节点自测试。
We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bell's inequalities with two measurement settings per observer are satisfied.
We give strong analytic and numerical evidence that, under mild measurement assumptions, two qubits cannot both be recycled to generate Bell nonlocality between multiple independent observers on each side. This is surprising, as under the same assumptions it is possible to recycle just one of the qubits an arbitrarily large number of times [P. J. Brown and R. Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. We derive corresponding 'one-sided monogamy relations' that rule out two-sided recycling for a wide range of parameters, based on a general tradeoff relation between the strengths and maximum…
The problem of characterizing classical and quantum correlations in networks is considered. Contrary to the usual Bell scenario, where distant observers share a physical system emitted by one common source, a network features several independent sources, each distributing a physical system to a subset of observers. In the quantum setting, the observers can perform joint measurements on initially independent systems, which may lead to strong correlations across the whole network. In this work, we introduce a technique to systematically map a Bell inequality to a family of Bell-type inequalities…
A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A unified framework to establish all kinds of CHSH-type Bell inequalities by increasing step by step the number of observers is given. As an application, compact Bell inequalities, for eight observers, involving just four correlation functions are proposed. They require much less experimental effort than standard methods and thus is experimentally friendly in mul…
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no-hidden-variables.
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…
Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network i.e. networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-ty…
Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal theory, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party randomly chooses three orthogonal measurements, then the parties will always violate a Bell inequality. Furthermore, we prove t…
A certain class of parametric down-conversion Bell type experiments has the following features. In the idealized perfect situation it is in only 50% of cases that each observer receives a photon; in the other 50% of cases one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts whether such experiments could be ever genuine tests of local realism. We propose to take into account these "unfavorab…
Entangled pure-states, Werner-states and generalized mixed-states of any structure, spanning a 2x2 Hilbert space are created by a novel high-brilliance universal source of polarization-entangled photon pairs. The violation of a Bell inequality has been tested for the first time with a pure-state, indeed a conceptually relevant ideal condition, and with Werner-states. The generalized ''maximally entangled mixed states'' (MEMS) were also synthetized for the first time and their exotic properties investigated by means of a quantum tomographic technique.
We investigate the scenario where an observer, Alice, shares a two-qubit state with an arbitrary number of observers, Bobs, via sequentially and independently recycling the qubit in possession of the first Bob. It is known that there exist entangled states which can be used to have an arbitrarily long sequence of Bobs who can violate the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. We show that there exist entangled states that do not violate the Bell inequality and whose entanglement can be detected by an arbitrary number of Bobs by suitably choosing the entangleme…
Quantum correlations arising in Bell experiments, involving a physical source that emits a quantum state to a number of observers, have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond the Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments c…
Quantum nonlocality may be an artifact of the assumption that observers obey the laws of classical mechanics, while observed systems obey quantum mechanics. I show that, at least in the case of Bell's Theorem, locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the Many-Worlds Interpretation. Using the MWI, I shall show that the apparently "non-local" expectation value for the product of the spins of two widely separated particles --- the "quantum" part of Bell's Theorem --- is really due to a series of three purely local measurements. Thus, experime…
Vaidman described how a team of three players, each of them isolated in a remote booth, could use a three-qubit Greenberger-Horne-Zeilinger state to always win a game which would be impossible to always win without quantum resources. However, Vaidman's method requires all three players to share a common reference frame; it does not work if the adversary is allowed to disorientate one player. Here we show how to always win the game, even if the players do not share any reference frame. The introduced method uses a 12-qubit state which is invariant under any transformation $R_a \otimes R_b \otim…
In this paper, the Lorentz transformation of entangled Bell states seen by a moving observer is studied. The calculated Bell observable for 4 joint measurements turns out to give a universal value, $<\hat{a}\otimes\vec{b}>+<\hat{a}\otimes\vec{b}'>+\lang le\hat{a}'\otimes\vec{b}> -<\hat{a}'\otimes\vec{b}'>=\frac{2}{\sqrt{2-β^2}}(1+\sqrt{1-\be ta^2})$, where $\hat{a}, \hat{b}$ are the relativistic spin observables derived from the Pauli-Lubanski pseudo vector and $β=\frac{v}{c}$. We found that the degree of violation of the Bell's inequality is decreasing with increasing velocity of the observer…
In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of nonlocal correlations in such a situation, when compared to those that can be generated in networks distributing independent local variables. We present an iterative procedure for constructing Bell inequalities tailored for networks: starting from a given network, and a corresponding Bell inequality, our technique provides new Bell inequalities for a more complex …
Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a \emph{correlation scenario}, and Bell's Theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from …
In the Greenberger-Horne-Zeilinger-Mermin (GHZM) proof of Bell's theorem, a source periodically emits an entangled state of three particles whose properties are analyzed by three distant observers and used to prove Bell's nonlocality theorem. This paper analyzes a somewhat different gedanken experiment involving only two observers that nevertheless makes indirect use of the GHZ states to prove Bell's theorem. The relationship of the GHZM proof to the present one is discussed, and it is pointed out that the latter provides an interesting new view of the connection between the "two theorems of J…
Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as "measurement independence" (also referred to as "freedom of choice" or "settings independence"). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence f…
We present a method to derive explicit forms of tight correlation function Bell inequalities for three systems and dichotomic observables, which involve three settings for each observer. We also give sufficient conditions for quantum predictions to satisfy the new inequalities.
Cabello has recently (in quant-ph/0210081) observed that ``...an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives.'' In this note I discuss the implications of this observation for tests of locality.
Quantized detector networks (QDN) deals with quantum information exchange between observers and their apparatus rather than with systems under observation. Partial observations in QDN involve subsets of the elementary signal detectors which constitute an apparatus. We use them to prove that QDN is consistent with Einstein locality and violations of Bell-type inequalities.
We investigate the scenario where spatially separated parties perform measurements in randomly chosen bases on an N-partite Greenberger-Horne-Zeilinger state. We show that without any alignment of the measurements, the observers will obtain correlations that violate a Bell inequality with a probability that rapidly approaches 1 as N increases and that this probability is robust against noise. We also prove that restricting these randomly chosen measurements to a plane perpendicular to a common direction will always generate correlations that violate some Bell inequality. Specifically, if each …
A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable quantum states. In addition, a quadratic inequality of the Bell operators for four-qubit systems is derived.
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are studied. It is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a facet of the more complex polytope.
Genuine Bell locality and nonlocality in the networks
本文研究网络中的真正Bell局域性与非局域性，提出涉及更多关联子的线性和非线性Bell型不等式，利用Pauli算符设计Bell测试并证明其最大违背，最后演示纠缠交换替代联合测量。
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。
We consider Bell tests involving bipartite states shared between three parties. We show that the simple inclusion of a third part may greatly simplify the measurement scenario (in terms of the number of measurement settings per part) and allows the identification of previously unknown nonlocal resources.
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each observer for a maximally entangled state and two observables for a non-maximally entangled state and write down appropriate inequalities and show violation by quantum examples. Finding an example for quadratures or position and momentum is left as an open problem.
We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger correlations stronger than previous Bell inequalities. For certain noise admixture to the correlations an explicit local realistic model exists in the case of a standard Bell experiment. Bell experiments with many local settings reveal the non-locality of the state. It turns out that the new inequality is more stringent than many other Bell inequalities in the …
The Bell basis, a set of maximally entangled biphoton state, is a critical prerequisite towards quantum information processing, and many quantum applications have highlighted the requirement for the manipulation of high-dimensional Bell basis. While the Bell states can be created by using ingenious single-photon quantum gates, its implementation complexity in higher dimensions is significantly increased. Here we present an elaborate approach to show that the adaptive pump modulation enable the efficient preparation of Bell basis in arbitrary-dimensional Hilbert space. A complete set of four-di…
Multipartite Bell-GHZ nonclassicality from interwoven frustrated down-conversion
该研究通过干涉过程展示多方参与贝尔-GHZ非经典性，利用受阻下转换源产生2N光子干涉，当至少一个本地下转换过程被阻断时，非经典性显现。
The chained Bell inequalities of Braunstein and Caves involving N settings per observer have some interesting applications. Here we obtain the minimum detection efficiency required for a loophole-free violation of the Braunstein-Caves inequalities for any N > 2. We discuss both the case in which both particles are detected with the same efficiency and the case in which the particles are detected with different efficiencies.
In an experiment designed to overcome the loophole of observer dependent reality and satisfying the counterfactuality condition, we measured polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and 1H(d,He) reactions in one setting. The results of these measurements are used to test the Bell and Wigner inequalties against the predictions of quantum mechanics.
We show that a single Bell's inequality with two dichotomic observables for each observer, which is originated from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin's theorem is proved in its most general form from which it follows that for pure states Bell's nonlocality and quantum entanglement are equivalent.
We demonstrate a novel approach of violating position dependent Bell inequalities by photons emitted via independent photon sources in free space. We trace this violation back to path entanglement created a posteriori by the selection of modes due to the process of detection.
We begin with a review of the famous thought experiment that was proposed by Einstein, Podolsky and Rosen (EPR) and mathematically formulated by Bell; the outcomes of which challenge the completeness of quantum mechanics and the locality of Nature. We then suggest a reinterpretation of the EPR experiment that utilizes observer complementarity; a concept from quantum gravity which allows spatially separated observers to have their own, independent reference frames. The resulting picture provides a self-consistent resolution of the situation that does not jeopardize causality nor unitarity, nor …
Non-locality and quantum measurement are two fundamental topics in quantum theory and theirinterplay attracts intensive focus since the discovery of Bell theorem. Non-locality sharing amongmultiple observers is predicted and experimentally observed. However, only one-sided sequentialcase, i.e., one Alice and multiple Bobs is widely discussed and little is known about two-sided case.Here, we theoretically and experimentally explore the non-locality sharing in two-sided sequentialmeasurements case in which one entangled pair is distributed to multiple Alices and Bobs. Weexperimentally observed d…
Bell-EPR Correlations within Local Quantum Theory
本文提出一种局部幺正理论，通过预测量过滤单光子偏振并结合四个光电探测器的检测过程，解释贝尔-爱因斯坦-波多尔斯基-罗森相关性，强调本地去相干与非本地解释的差异。
In this paper we show a Bell inequality of Clauser-Horne type for three three-dimensional systems (qutrits). Violation of the inequality by quantum mechanics is shown for the case in which each of the three observers measures two non-commuting observables, defined by the so called unbiased symmetric six port beamsplitters, on a maximally entangled state of three qutrits. The strength of the violation of the inequality agrees with the numerical results presented in Kaszlikowski et. al., quant-ph//0202019.
Bell-Mermin-Klyshko Inequalities and One-way Information Deficit of Dirac Fields in Noninertial Frames
本研究针对非惯性系中狄拉克场，结合乌伦贝克效应下惯性与加速观察者的量子关联，推导特定量子态单向信息赤字的部分解析结果并给出贝尔-默明-克吕什科不等式的数值结果，揭示了贝尔非定域性及单向信息赤字在相对论量子信息中的意义。
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