Bell's Theorem Research Articles

Penrose Dodecahedron, Witting Configuration and Quantum Entanglement

A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose for formulation of analogue of Bell theorem without probabilities. The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. However, such reformulation needs for some subtleties related with entanglement of two such configurations essential for consideration of non-locality and some other questions. Two entangled systems with quantum states described by Witting configurations are discussed in the present work. Duplication of points with respect to vertices of dodecahedron produces rather significant increase with number of symmetries in 25920/60=432 times. Quantum circuits model is a natural language for description of operations with different states and measurements of such systems.Quanta 2024; 13: 38–46.

RADIAL ASYMPTOTICS OF GENERATING FUNCTIONS OF k-REGULAR SEQUENCES

AbstractWe give a new proof of a theorem of Bell and Coons [‘Transcendence tests for Mahler functions’, Proc. Amer. Math. Soc.145(3) (2017), 1061–1070] on the leading order radial asymptotics of Mahler functions that are the generating functions of regular sequences. Our method allows us to provide a description of the oscillations whose existence was shown by Bell and Coons. This extends very recent results of Poulet and Rivoal [‘Radial behavior of Mahler functions’, Int. J. Number Theory, to appear].

Measurement Dependence can Affect Security in a Quantum Network

AbstractNetwork Nonlocality is an advanced study of quantum nonlocality that comprises network structure beyond Bell's theorem. The development of quantum networks has the potential to bring a lot of technological applications in several quantum information processing tasks. Here, the focus is on how the role of the independence of the measurement choices by the end parties in a network works and can be used to affect the security in a quantum network. In both three‐parties two‐sources bilocal network and four‐parties three‐sources star network scenarios, this study is able to show, a practical way to understand the relaxation of the assumptions to enhance a real security protocol if someone wants to breach in a network communication. Theoretically, it have been proved that by relaxing the independence of the measurement choices of only one end party, a Standard Network Nonlocality (SNN) and more stronger Full Network Nonlocality (FNN) can be created and the maximum quantum violation by the classical no‐signalling local model can be obtained. The distinguish between two types of network nonlocality, SNN and FNN, can also be made. It has been shown that FNN is a stronger correlation than SNN in the sense that the former comes in a scenario where all the sources must be nonlocal in nature.

Alternative Einstein-Podolsky-Rosen argument based on premises not falsified by Bell's theorem: weak macroscopic realism and weak local realism

Alternative Einstein-Podolsky-Rosen argument based on premises not falsified by Bell's theorem: weak macroscopic realism and weak local realism

Loophole-Free Test of Local Realism via Hardy's Violation.

Bell's theorem states that the quantum mechanical description of physical quantities cannot be fully explained by local realistic theories, laying a solid basis for various quantum information applications. Hardy's paradox is celebrated as the simplest form of Bell's theorem concerning its "All versus Nothing" approach to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of the experimental systems, and these assumptions constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source. By achieving a detection efficiency of 82.2%, a quantum state fidelity of 99.10%, and applying high-speed quantum random number generators for the measurement setting switching, the experiment is implemented in a loophole-free manner. During 6h of running, a strong violation of P_{Hardy}=4.646×10^{-4} up to 5 standard deviations is observed with 4.32×10^{9} trials. A null hypothesis test shows that the results can be explained by local realistic theories with an upper bound probability of 10^{-16348}. These testing results provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.

Does Quantum Mechanics Require "Conspiracy"?

Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show that excluding them requires a fine-tuning to an extremely restricted subspace of the Hilbert space that seems "conspiratorial", in the sense that (1) it seems to depend on future events that involve records (including measurement settings) and on the dynamical law (normally thought to be independent of the initial conditions), and (2) it violates Statistical Independence, even when it is valid in the context of Bell's theorem. To solve the puzzle, I build a model in which, by changing the dynamical law, the same initial conditions can lead to different histories in which the validity of records is relative to the new dynamical law. This relative validity of the records may restore causality, but the initial conditions still must depend, at least partially, on the dynamical law. While violations of Statistical Independence are often seen as non-scientific, they turn out to be needed to ensure the validity of records and our own memories and, by this, of science itself. A Past Hypothesis is needed to ensure the existence of records and turns out to require violations of Statistical Independence. It is not excluded that its explanation, still unknown, ensures such violations in the way needed by local interpretations of quantum mechanics. I suggest that an as-yet unknown law or superselection rule may restrict the full tensor-product Hilbert space to the very special subspace required by the validity of records and the Past Hypothesis.

The photonic content of a transmission-line pulse

We develop a photonic description of short, one-dimensional electromagnetic pulses, specifically in the language of electrical transmission lines. Current practice in quantum technology, using arbitrary waveform generators, can readily produce very short, few-cycle pulses in a very-low-noise, low-temperature setting. We argue that these systems attain the limit of producing pure coherent quantum states, in which the vacuum has been displaced for a short time, and therefore over a short spatial extent. When the pulse is bipolar, that is, the integrated voltage of the pulse is zero, then the state can be described by the finite displacement of a single mode. Therefore there is a definite mean number of photons, but which have neither a well-defined frequency nor position. Due to the Paley-Wiener theorem, the two-component photon "wavefunction" of this mode, while somewhat localized, is not strictly bounded in space even if the vacuum displacement that defines it is bounded. When the pulse is unipolar, no photonic description is possible-the photon number can be considered to be divergent. We consider properties that photon counters and quantum non-demolition detectors must have to optimally convert and detect the photons in several example pulses. We develop a conceptual test system for implementing short-pulse quantum key distribution, building on the design of a recently achieved Bell's theorem test in a cryogenic microwave setup.

The Method of Everything vs. Experimenter Bias of Loophole-Free Bell Experiments.

Experimenter bias compromises the integrity and advancement of science, especially when awarded as such. For example, the 2022 Nobel Prize in Physics awarded for the loophole-free experiments that tested physicist John S. Bell's inequality theorem. These experiments employed the logic of conducting local experiments to obtain local evidence that contradicted local realistic theories of nature, thereby validating quantum mechanics as a fundamental non-local theory. However, there was one loophole that was wittingly not tested by the Nobel laureates. The notable exception was Bell's "super-deterministic" loophole, which was validated (2000) (2001) (2002) (2003) (2004) (2005) (2006) (2007) (2008) (2009) (2010) (2011) (2012) non-locally, thus compromising the subsequent Nobel Prize. More importantly, the discovery of two mutually exclusive and jointly exhaustive non-local hidden variables revealed why local scientific methods obtain false-positive and false-negative results. With knowledge of this fundamental omission, the inclusion of the non-local hidden variables in the local methods used in science can then advance it to be a complete study of nature.

Classical Information and Collapse in Wigner's Friend Setups.

The famous Wigner's friend experiment considers an observer-the friend-and a superobserver-Wigner-who treats the friend as a quantum system and her interaction with other quantum systems as unitary dynamics. This is at odds with the friend describing this interaction via collapse dynamics, if she interacts with the quantum system in a way that she would consider a measurement. These different descriptions constitute the Wigner's friend paradox. Extended Wigner's friend experiments combine the original thought experiment with non-locality setups. This allows for deriving local friendliness inequalities, similar to Bell's theorem, which can be violated for certain extended Wigner's friend scenarios. A Wigner's friend paradox and the violation of local friendliness inequalities require that no classical record exists, which reveals the result the friend observed during her measurement. Otherwise, Wigner agrees with his friend's description and no local friendliness inequality can be violated. In this article, I introduce classical communication between Wigner and his friend and discuss its effects on the simple as well as extended Wigner's friend experiments. By controlling the properties of a (quasi) classical communication channel between Wigner and the friend, one can regulate how much outcome information about the friend's measurement is revealed. This gives a smooth transition between the paradoxical description and the possibility of violating local friendliness inequalities, on the one hand, and the effectively collapsed case, on the other hand.

Bell's theorem in time without inequalities

Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by correlated measurement statistics of quantum mechanics. Greenberger, Horne, and Zeilinger (GHZ) gave a more compelling proof of Bell's theorem without inequalities by considering perfect correlations rather than statistical correlations. In this work, we present a temporal analogue of GHZ argument that establishes Bell's theorem in time without inequalities.

Contra Bellum: Bell's Theorem as a Confusion of Languages

Bell's theorem is a conflict of mathematical predictions formulated within an infinite hierarchy of mathematical models. Inequalities formulated at level $k\in\mathbb{Z}$, are violated by probabilities at level $k+1$. We are inclined to think that $k=0$ corresponds to the the classical world, while the quantum one is $k=1$. However, as the $k=0$ inequalities are violated by $k=1$ probabilities, the same relation holds between $k=1$ inequalities violated by $k=2$ probabilities, $k=-1$ inequalities, violated by $k=0$ probabilities, and so forth. Accepting the logic of the Bell theorem, can we prove by induction that nothing exists?

Distilling Nonlocality in Quantum Correlations.

Nonlocality, as established by the seminal Bell's theorem, is considered to be the most striking feature of correlations present in spacelike separated events. Its practical application in device independent protocols, such as secure key distribution, randomness certification, etc., demands identification and amplification of such correlations observed in the quantum world. In this Letter we study the prospect of nonlocality distillation, wherein, by applying a natural set of free operations (called wirings) on many copies of weakly nonlocal systems, one aims to generate correlations of higher nonlocal strength. In the simplest Bell scenario, we identify a protocol, namely, logical OR-AND wiring, that can distill nonlocality to a significantly high degree starting from arbitrarily weak quantum nonlocal correlations. As it turns out, our protocol has several interesting facets: (i)it demonstrates that a set of distillable quantum correlations has nonzero measure in the full eight-dimensional correlation space, (ii)it can distill quantum Hardy correlations by preserving its structure, (iii)it shows that (nonlocal) quantum correlations sufficiently close to the local deterministic points can be distilled by a significant amount. Finally, we also demonstrate efficacy of the considered distillation protocol in detecting postquantum correlations.

Witnessing Nonclassicality in a Causal Structure with Three Observable Variables

Seen from the modern lens of causal inference, Bell's theorem is nothing else than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell's paradigmatic scenario and consider different causal structures. For the specific case of three observable variables, it is known that there are three non-trivial causal networks. Two of those, are known to give rise to quantum non-classicality: the instrumental and the triangle scenarios. Here we analyze the third and remaining one, which we name the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove a number of results about this elusive scenario and introduce new and efficient computational tools for its analysis that also can be adapted to deal with more general causal structures. We do not solve its main open problem -- whether quantum non-classical correlations can arise from it -- but give a significant step in this direction by proving that post-quantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.

Deterministic Interpretation of the Malus Law and Correlation in Experiments with Entangled Photons

This paper examines a local deterministic model of an experiment involving correlated photons. The experimental setup involves a source that emits two linearly polarized photons in each act, two two-channel analyzers, and detectors included in the coincidence scheme. The orientation angle of the photon polarization plane is a random variable with a uniform distribution, and it is the same for simultaneously emitted photons. The model presented here is a generalization of the “naive example of hidden variable theory” described in A. Aspect's article ‘Bell's Theorem: The Naive View of an Experimentalist.
 In our model, the outcome of the photon interaction with the analyzer (hit in one of the two channels) is uniquely determined by the angle between the photon polarization plane and the analyzer axis and is described by a step function. The difference in our model is that the step function contains a large number of segments of different lengths. The location and lengths of the segments are set so that the probability of a photon hitting a specific channel of an ideal analyzer, determined by averaging the outcomes over small neighborhoods of angles, approaches the Malus law when the maximum length of a segment decreases. This ensures that the classical model is self-consistent.
 When ideal analyzers are used, the absolute value of the correlation coefficient of detector readings mainly does not exceed the values from Aspect's ‘naive example’. However, when analyzers with absorption are used, the calculated correlations for some orientations of the analyzers exceed the quantum mechanical values. Key words: linear polarization of photons, Malus law, entangled photons, correlations, hidden parameters.

On the ontological ambiguity of physics facing reality

AbstractWe discuss in this work, the contradictory position in modern Physics between the existence of a microphysical quantum reality and macrophysical classical one. After discussing some basic concepts in Philosophy, we revisit the situation of Quantum Mechanics results, particularly after the confirmation of violations of Bell's theorem, and its significance to create a tension between the micro and the macro world, which is very fundamental and unsolved.

How and when did locality become ‘local realism’? A historical and critical analysis (1963–1978)

The history of the debates on the foundational implications of the Bell non-locality theorem displayed very soon a tendency to put the theorem in a perspective that was not entirely motivated by its very assumptions, in particular in terms of a ‘local-realistic’ narrative, according to which a major target of the theorem would be the very possibility to conceive quantum theory as a theory concerning ‘real’ stuff in the world out-there. I present here a historico-critical analysis of the stages, between 1963 and 1978, through which the locality condition of the original Bell theorem almost undiscernibly turned into a ‘local realism’ condition, a circumstance which too often has affected the analysis of how serious the consequences of the Bell theorem turn out to be. In particular, the analysis puts into focus the interpretive oscillations and inconsistencies surrounding ‘local realism’, that emerge in the very descriptions that many leading figures provided themselves of the deep work they devoted to the theorem and its consequences.

Characterization of nonsignaling bipartite correlations corresponding to quantum states

Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.

Alain Aspect’s experiments on Bell’s theorem: a turning point in the history of the research on the foundations of quantum mechanics

Alain Aspect's three experiments on Bell's theorem, published in the early 1980s, were a turning point in the history of the research on the foundations of quantum mechanics not only because they corroborated entanglement as the distinctive quantum signature but also because these experiments brought wider recognition to this field of research and Aspect himself. These experiments may be considered the most direct precursors of the research on quantum information, which would blossom a decade later.

$$\psi $$-Epistemic models and the Bell theorem

We consider a question in what condition a mixed state which can be decomposed in different ways cannot be described by a single set of hidden variables. The condition is closely related with Bell theorem.

Quantum violation of average causal effects in multiple measurement settings

Estimating causal relations from observed correlations is a central content of science. Although a comprehensive mathematical framework has been developed to identify cause and effect, it is well known that such methods and techniques are not applicable to quantum systems due to Bell's theorem. Generally, the incompatibility between quantum correlation and classical causal theory is illustrated by the violation of Bell inequality. Gachechiladze provides a new method called the violation of lower bound of average causal effect (ACE) to witness the incompatibility. We consider a new lower bound of ACE derived by Cao in multiple measurement settings. We show that there are always pure entangled states and incompatible projective measurements that can generate correlations that violate this new classical lower bound. In Gachechiladze's work, the measurement settings are binary, while the measurement settings in our paper are $K$-ary ($K\ensuremath{\ge}2$) and we give more general conclusions. When $K=2$, the same result as in Gachechiladze's work can be obtained.