Jing-Ling Chen, Dagomir Kaszlikowski, L. C. Kwek, Marek Zukowski, C. H. Oh
In Kaszlikowski [Phys. Rev. Lett. {\bf 85}, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled $N$-dimensional ($3 \leq N$) quantum objects is stronger than for two maximally entangled qubits and grows with $N$. In this paper we present the analytical proof of this fact for N=3.
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We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.
We report two fundamental experiments on three-level quantum systems (qutrits). The first one tests the simplest task for which quantum mechanics provides an advantage with respect to classical physics. The quantum advantage is certified by the violation of Wright's inequality, the simplest classical inequality violated by quantum mechanics. In the second experiment, we obtain contextual correlations by sequentially measuring pairs of compatible observables on a qutrit, and show the violation of Klyachko et al.'s inequality, the most fundamental noncontextuality inequality violated by qutrits.…
It is shown that the model introduced by Cabello et al. to criticize the Franson experiment suffers from the same weakness as the previous model introduced by Aerts et al. with the same purpose. It is also shown why we can assume with confidence that the Franson experiment does violate local realism.
We suggest to test the premise of ``macroscopic local realism'' which is sufficient to derive Bell inequalities when measurements of photon number are only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of ``macroscopic local realism''. Quantum states violating th…
A sequence of Bell inequalities for N-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zeilinger states, quantum mechanics violates these inequalities by factors exponentially growing with N. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as (2/3)^N.
We formulate a two-party communication complexity problem and present its quantum solution that exploits the entanglement between two qutrits. We prove that for a broad class of protocols the entangled state can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bell's inequality for two qutrits.
Identical, independent quantum weak measurements violate objective realism
本文通过无约束弱测量验证量子世界中的客观实在论矛盾，利用两个相同且独立的弱探测器和最终条件化，实验在IBM和IonQ公开量子计算机上完成，结果在10个标准差水平上观察到违反，同时验证了主要量子硬件供应商的参数双量子位门质量。
Recently, [{arXiv:0810.3134}] is accepted and published. We show that local realistic theories violate separability of $N$-qubit quantum states by a factor of $3^N$. Thus we have a violation factor of 3 when N=1. Realistic theories violate a proposition of a single qubit (a state with two-dimensional space) system, the Bloch sphere machinery of quantum mechanics. Our method uses the ratio of each of the scalar products. The maximal possible value of the scalar product in local realistic theories grows exponentially larger than one in $N$-qubit separable states when the number of qubits increas…
In this brief report we show the new Bell-Clauser-Horne inequality for two entangled three dimensional quantum systems (so called qutrits). This inequality is violated by a maximally entangled state of two qutrits observed via symmetric three input and three output port beamsplitter only if the amount of noise in the system equals ${11-6\sqrt3 \over 2}\approx 0.308$. This is in perfect agreement with the previous numerical calculations presented in Kaszlikowski {\it et. al.} Phys. Rev. Lett. {\bf 85}, 4418 (2000).
Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits
本文基于解析表达式和大量数值验证，发现任意两自旋三态量子比特态在局域自旋-1测量下均不违反CHSH不等式，并比较了并发度与CHSH参数，揭示了与自旋-1/2情形的差异。
CHSH inequality always holds in bipartite qutrits with spin-1 observables
该研究证明在双粒子三能级系统中，所有态在自旋-1测量下均满足CHSH不等式，解决了关于非纠缠态不违反该不等式的猜想。
Mermin inequalities are derived for systems of three-state particles (qutrits) employing three local measurement settings. These establish perfect correlations which violate local realistic bounds more strongly than those previously reported with two bases. The quantum eigenvalue of the Mermin operator grows as the dimension of the Hilbert space, $3^N$, rather than $2^N$, as obtained with two measurement bases. The number of distinct GHZ contradictions also increases as $3^N$.
In a recent paper [arXiv:1301.2887] Ahrens et al. claim that our "(...) experiment on qutrits does not test Klyachko et al.'s inequality, but an inequality with extra correlations" and that the "(...) experiment cannot be considered a proper test of a noncontextuality inequality, since the same observable is measured with different setups in different contexts". We disagree with these claims. In this note we briefly re-state how our test of the non-contextuality inequality was constructed. We explain how we keep the context of measurements when switching between different terms of the tested i…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such …
Bell-Clauser-Horne-Shimony-Holt inequality (in terms of correlation functions) of two qutrits is studied in detail by employing tritter measurements. A uniform formula for the maximum value of this inequality for tritter measurements is obtained. Based on this formula, we show that non-maximally entangled states violate the Bell-CHSH inequality more strongly than the maximally entangled one. This result is consistent with what was obtained by Ac{í}n {\it et al} [Phys. Rev. A {\bf 65}, 052325 (2002)] using the Bell-Clauser-Horne inequality (in terms of probabilities).
We show that failure of local realism can be revealed to observers for whom only extremely coarse-grained measurements are available. In our instances, Bell's inequality is violated even up to the maximum limit while both the local measurements and the initial local states under scrutiny approach the classical limit. Furthermore, we can observe failure of local realism when an inequality enforced by non-local realistic theories is satisfied. This suggests that locality alone may be violated while realism cannot be excluded for specific observables and states. Small-scale experimental demonstra…
I argue that quantum mechanics is a realistic theory, but it violates either strong locality (no superluminal influences) or strict causality (diiferent effects cannot follow from the same cause).
In the celebrated paper [J. Phys. A: Math. Gen. 37, 1775 (2004)], D. Collins and N. Gisin presented for the first time a three setting Bell inequality (here we call it CG inequality for simplicity) which is relevant to the Clauser-Horne-Shimony-Holt (CHSH) inequality. Inspired by their brilliant ideas, we obtained some multi-setting tight Bell inequalities, which are relevant to the CHSH inequality and the CG inequality. Moreover, we generalized the method in the paper [Phys.Rev. A 79, 012115 (2009)] to construct Bell inequality for qubits to higher dimensional system. Based on the generalized…
It has been well established that quantum mechanics (QM) violates Bell inequalities (BI), which are consequences of local realism (LR). Remarkably QM also violates Leggett inequalities (LI), which are consequences of a class of nonlocal realism called crypto-nonlocal realism (CNR). Both LR and CNR assume that measurement outcomes are determined by preexisting objective properties, as well as hidden variables (HV) not considered in QM. We extend CNR and LI to include the case that the measurement settings are not externally fixed, but determined by hidden variables (HV). We derive a new version…
There is no doubt about the fact that entanglement and nonlocality are distinct resources. It is acknowledged that a clear illustration of this point is the difference between maximally entangled states and states that maximally violate a Bell inequality. We give strong evidence that this anomaly may be an artefact of the measures that have been used to quantify nonlocality. By reasoning that the numeric value of a Bell function is akin to a witness rather than a quantifier, we define a measure of nonlocality and show that, for pairs of qutrits and of four-level systems, maximal entanglement d…
We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals non-classicality for a larger set of quantum states. Finally, we find that like probability based inequalities, entropic ones are maximally violated by the non-maximally entangled qutrit state.
We present a linear program that is capable of determining whether a set of correlations can be captured by a local realistic model. If the correlations can be described by such a model, the linear program outputs a joint probability distribution that produces the given correlations. If the correlations cannot be described under the assumption of local realism, the program outputs a Bell inequality violated by the correlations.
Local realism in recent experiments is excluded on condition of freedom or randomness of choice combined with no signaling between observers by implementations of simple quantum models. Both no-signaling and the underlying quantum model can be directly checked by analysis of experimental data. For particular tests performed on the data, it is shown that two of these experiments give the probability of the data under no-signaling (or choice independence in one of them) hypothesis at the level of 5%, accounting for the look-elsewhere-effect, moderately suggesting that no-signaling is violated wi…
Chen (quant-ph/0611126) has recently claimed ``exponential violation of local realism by separable states", in the sense that multi-partite separable quantum states are supposed to give rise to correlations and fluctuations that violate a Bell-type inequality that Chen takes to be satisfied by local realism. However, this can not be true since all predictions (including all correlations and fluctuations) that separable quantum states give rise to have a local realistic description and thus satisfy all Bell-type inequalities, and this holds for all number of parties. Since Chen claims otherwise…
Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-Massar-Popescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yieldi…
We put bounds on the minimum detection efficiency necessary to violate local realism in Bell experiments. These bounds depends of simple parameters like the number of measurement settings or the dimensionality of the entangled quantum state. We derive them by constructing explicit local-hidden variable models which reproduce the quantum correlations for sufficiently small detectors efficiency.
The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing …
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated…
Are Bell's conditions for local realism general enough?
本文重新审视贝尔局域现实条件，提出更现实的物理条件以实现违反贝尔不等式的光学实验模型。
Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open chal…
We present numerical data showing, that three qutrit correlations for a pure state, which is not maximally entangled, violate local realism more strongly than three-qubit correlations. The strength of violation is measured by the minimal amount of noise that must be admixed to the system so that the noisy correlations have a local and realistic model.
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be esti…
Macro-realism is the position that certain "macroscopic" observables must always possess definite values: e.g. the table is in some definite position, even if we don't know what that is precisely. The traditional understanding is that by assuming macro-realism one can derive the Leggett-Garg inequalities, which constrain the possible statistics from certain experiments. Since quantum experiments can violate the Leggett-Garg inequalities, this is taken to rule out the possibility of macro-realism in a quantum universe. However, recent analyses have exposed loopholes in the Leggett-Garg argument…
Recent experiments of Groeblacher et al. proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Groeblacher…
Cluster states are a new type of multiqubit entangled states with entanglement properties exceptionally well suited for quantum computation. In the present work, we experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism. This exploration is based on a recently derived Bell-type inequality [V. Scarani et al., Phys. Rev A 71, 042325 (2005)] which is tailored, by using a combination of three- and four-particle correlations, to be maximally violated by cluster states but not violated at all by GHZ states. We observe a cluster state Be…
The assumption of local realism in a Bell locality scenario imposes non-trivial conditions on the Shannon entropies of the associated probability distributions, expressed by linear entropic Bell inequalities. In principle, these entropic inequalities provide necessary but not sufficient criteria for the existence of a local hidden variable model reproducing the correlations, as, for example, the paradigmatic nonlocal PR-box is entropically not different from a classically correlated box. In this paper we show that for the n-cycle scenario, entropic inequalities completely characterize the set …
The Bell's inequalities are derived from the hypotheses of Locality, Realism and (what is lesser known) the equality between the factual and the counterfactual time averages of the expectation values of observables. The necessity of a hypothesis additional to Local Realism opens a promising way out to the old controversy between Quantum Mechanics and Local Realism. For, it is possible to speculate that it is this additional hypothesis, and not Local Realism, what is disproved in the experiments reporting the violation of the Bell's inequalities. Yet, there are doubts on how the additional hypo…
Most working scientists hold fast to the concept of 'realism' - a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenabl…
Recently much interest has been directed towards designing setups that achieve realistic loss thresholds for decisive tests of local realism, in particular in the optical regime. We analyse the feasibility of such Bell tests based on a W-state shared between multiple parties, which can be realised for example by a single photon shared between spatial modes. We develop a general error model to obtain thresholds on the efficiencies required to violate local realism, and also consider two concrete optical measurement schemes.
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…
We present Bell inequalities for graph states with high violation of local realism. In particular, we show that there is a two-setting Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of two. These inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. We first present a method which assigns a Bell inequality for each graph vertex. Then for some families of graph states composite Bell inequalities can be constructed with a violation of local realism increasing exponen…
Almost all Bell-inequality experiments to date have used postselection, and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorises…
We consider the so called Legget inequalities which are deduced from the assumption of general (local or non-local) realism plus the arrow of time preservation. Then, instead of assuming cryto-nonlocal hidden variables, we assume any (local or non-local) realism compatible with the joint and non-joint expected values dictated by quantum mwechaanics. Hence, we prove that this double assumption is not consistent, since the corresponding general Leggett inequalities are violated by quantum mechanics. Thus, realism plus arrow of time preservation and quntum mechanics are not compatible. In other w…
In a local realist world view, physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described within local realism. Such experiments usually require additional assumptions that make them vulnerable to a number of "loopholes." A recent experiment [Giustina et al, Nature, 2013] violated a Bell inequality without being vulnerable to the detection (or fair-sampling) loophole, therefore not needing the fair-sampling assump…
It has been experimentally confirmed that quantum physical phenomena can violate the Information Bell Inequalities. A violation of the one or the other of these Information Bell Inequalites is equivalent to a violation of local realism meaning that either objectivity or locality, or both, do not hold for the phenomena under investigation. We propose (1) an experimental design for carrying out classical measurements in the absence of ontological complementarity; (2) a rational way to extract epistemologically complementary (pseudocomplementary) data from it; (3) a statistical approach which can…
We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness o…
Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger that that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does not violate locality, but does violate realism.
Violation of Bell-type Inequality in the Hanbury Brown-Twiss (HBT) Toy-Model: Quantum Correlations beyond Local-Realism
该研究构建了简化的4模HBT玩具模型，通过适配的贝尔型不等式验证其关联违反不等式，证明存在非局域量子特性，凸显简化模型在研究光学系统非经典性中的作用。
Permutation asymmetry unlocks emergent advantage in randomized Bell tests
研究发现最大纠缠两量子比特态的置换不对称性导致其在随机贝尔测试中非局域性表现不同，不对称态可提高非局域性观测概率，并揭示测量选择相关性。
Most physicists uphold that the tests of the Bell inequalities (BI) performed up to now confirm the predictions of standard quantum mechanics (SQM) and refute local realism. But some scholars criticize this conviction, defending local realism in various ways. We present here a new viewpoint based on an improved version of the extended semantic realism (ESR) model that has been recently worked out by one of the authors. The ESR model embodies the mathematical formalism of SQM into a more general framework in which not only local realism but also objectivity of physical properties holds, and the…
Bell type inequalities are used to test local realism against quantum theory.In this paper, we consider a two party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated by quantum theory by a factor of 1.522 tolerating 0.586 fraction of white noise admixture which is twice that of the previous results.
Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumpt…
The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur independently of being observed. Giving up any one of these two beliefs (usually known together as Local Realism) is controversial. Many theories have been proposed to reconcile the violation of Bell's inequalities with Local Realism, but none has been fully successful. In this paper, it is recalled that any theory aimed to violate Bell's inequalities must start by g…
A family of Bell-type inequalities is present, which are constructed directly from the "standard" Bell inequalities involving two dichotomic observables per site. It is shown that the inequalities are violated by all the generalized Greenberger-Horne-Zeilinger states of multiqubits. Remarkably, our new inequalities can provide stronger non-locality tests in a sense that the local reality inequalities are exponentially stronger than the corresponding multipartite separability inequalities. This reveals that the exponential violation of local realism by separable states is an interesting consequ…
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.
In this paper we extend the ladder proof of nonlocality without inequalities for two spin-half particles given by Boschi et al [PRL 79, 2755 (1997)] to the case in which the measurement settings of the apparatus measuring one of the particles are different from the measurement settings of the apparatus measuring the other particle. It is shown that, in any case, the proportion of particle pairs for which the contradiction with local realism goes through is maximized when the measurement settings are the same for each apparatus. Also we write down a Bell inequality for the experiment in questio…
Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequali…
Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule imposes a constraint on feasible local operations. As we show in an example, the necessary particle entanglement might solely result from their indistinguishability. Our result reveals a fundamental relation between the non-locality and the particle entanglement.
We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector-efficiency, which makes a strong case for a loophole-free test.
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