Bell Inequality Research Articles

Quantum Nonlocality: How Does Nature Do It?

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space-time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other's state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell-CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter's freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole.

Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

We investigate the entanglement in a two-particle system with continuous degree of freedom constituted by trapped neutral atoms interacting via tunable dipole-dipole interaction. We describe the system in the quantum Wigner phase space representation. The atom entanglement is measured in terms of violation of the non separability condition or of some Bell inequalities. By an optimal control procedure, we design the control parameters that steer the system toward a maximally entangled state. We estimate the robustness of the control by considering the presence of an external source of noise weakly interacting with the atoms.

New observables for testing Bell inequalities in W boson pair production

We show that testing Bell inequalities in W± pair systems by measuring their angular correlation suffers from the ambiguity in kinetical reconstruction of the dilepton decay mode. We further propose a new set of Bell observables based on the measurement of the linear polarization of the W bosons that can be used in the semileptonic decay mode of W± pair, and we analyze the prospects of testing the violation of Bell inequalities at e+e− colliders. Published by the American Physical Society 2024

Fermionic steering is not nonlocal in the background of dilaton black hole

We study the redistribution of the fermionic steering and the relation among fermionic Bell nonlocality, steering, and entanglement in the background of the Garfinkle–Horowitz–Strominger dilaton black hole. We analyze the meaning of the fermionic steering in terms of the Bell inequality in curved spacetime. We find that the fermionic steering, which is previously found to survive in the extreme dilaton black hole, cannot be considered to be nonlocal. We also find that the dilaton gravity can redistribute the fermionic steering, but cannot redistribute Bell nonlocality, which means that the physically inaccessible steering is also not nonlocal. Unlike the inaccessible entanglement, the inaccessible steering may increase non-monotonically with the dilaton. Furthermore, we obtain some monogamy relations between the fermionic steering and entanglement in dilaton spacetime. In addition, we show the difference between the fermionic and bosonic steering in curved spacetime.

Probing entanglement and testing Bell inequality violation with e+e−→τ+τ− at Belle II

We present a feasibility study to probe quantum entanglement and Bell inequality violation in the process e+e−→τ+τ− at a center-of-mass energy of s=10.579 GeV. The sensitivity of the analysis is enhanced by applying a selection on the scattering angle ϑ in the τ+τ− center-of-mass frame. We analyze events in which both τ leptons decay to hadrons, using a combination of decay channels τ−→π−ντ, τ−→π−π0ντ, and τ−→π−π+π−ντ. The spin orientation of the τ leptons in these decays is reconstructed using the polarimeter-vector method. Assuming a dataset of 200 million τ+τ− events and accounting for experimental resolutions, we expect the observation of quantum entanglement and Bell inequality violation by the Belle-II experiment will be possible with a significance well in excess of five standard deviations. Published by the American Physical Society 2024

Hidden Tensor Structures.

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration can be decomposed into an arbitrary number of subsystems. The resulting structure is rich enough to enable quantum computation, violation of Bell's inequalities, and formulation of universal quantum gates. Less standard quantum applications involve a distinction between position and hidden position. The hidden position can be accompanied by a hidden spin, even if the particle is spinless. Hidden degrees of freedom are, in many respects, analogous to modular variables. Moreover, it is shown that these hidden structures are at the roots of some well-known theoretical constructions, such as the Brandt-Greenberg multi-boson representation of creation-annihilation operators, intensively investigated in the context of higher-order or fractional-order squeezing. In the context of classical signal analysis, the discussed structures explain why it is possible to emulate a quantum computer by classical analog circuit devices.

Corrected Bell and non-contextuality inequalities for realistic experiments.

Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a non-classical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property of non-signalling or non-disturbance, and the latter by the empirical property of measurement sharpness. However, in realistic experiments neither empirical property holds exactly, which leads to possible objections to contextuality as a form of non-classicality, and potential vulnerabilities for supposed quantum advantages. We introduce measures to quantify both properties, and introduce quantified relaxations of the corresponding assumptions. We prove the continuity of a known measure of contextuality, the contextual fraction, which ensures its robustness to noise. We then bound the extent to which these relaxations can account for contextuality, via corrections terms to the contextual fraction (or to any non-contextuality inequality), culminating in a notion of genuine contextuality, which is robust to experimental imperfections. We then show that our result is general enough to apply or relate to a variety of established results and experimental set-ups. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time.

The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice and arrow-of-time. It turns out that nature violates Bell inequalities, which implies the failure of at least one of those assumptions. Since rejecting any of them, even partially, is sufficient to explain the observed correlations, it is natural to inquire about the cost in each case. This paper builds upon the findings in Blasiak et al. 2021 Proc. Natl Acad. Sci. USA 118, e2020569118 (doi:10.1073/pnas.2020569118) showing the equivalence between the locality and free choice assumptions. Here, we include retrocausal models to complete the picture of causal explanations of the observed correlations. Furthermore, we refine the discussion by considering more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Quantifying Bell nonlocality of a pure two-qudit state via its entanglement

For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in Loubenets and Namkung (2022 J. Phys. A: Math. Theor. 55 285301) and also expressed via the concurrence, analytically quantify Bell nonlocality of a pure two-qudit state via its entanglement, in particular, prove explicitly that entanglement of a pure two-qudit state is necessary and sufficient for its Bell nonlocality. By re-visiting the pure two-qubit case, we also find and rigorously prove the new results on correlation properties of an arbitrary pure two-qubit state.

Quantum nonlocality evolution for two entangled mesoscopic fields under decoherence

Investigation of the nonlocality evolution of entangled mesoscopic fields under decoherence not only is important for understanding the quantum–classical transition, but also has relevance to quantum communication and quantum computation protocols based on continuous variables. According to previous formulations of Bell inequalities, the system loses nonlocal features far before the disappearance of entanglement. We here construct a new version of Bell signal based on rotated and displaced on–off correlations, with which the Bell inequality is violated as long as there remains entanglement and the field state components keep quasiorthogonal. Consequently, the nonlocal character revealed by our formulation decays much slower compared with those based on previous ones. More importantly, there exists a wide regime where the Bell inequality is restored with previous formulations but remains to be violated based on our correlation operators.

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.

Generation of entangled photon pairs from a silicon bichromatic photonic crystal cavity

Integrated quantum photonics leverages the on-chip generation of nonclassical states of light to realize key functionalities of quantum devices. Typically, the generation of such nonclassical states relies on whispering gallery mode resonators, such as integrated optical micro-rings, which enhance the efficiency of the underlying spontaneous nonlinear processes. While these kinds of resonators excel in maximizing either the temporal confinement or the spatial overlap between different resonant modes, they are usually associated with large mode volumes, imposing an intrinsic limitation on the efficiency and footprint of the device. Here, we engineer a source of time-energy entangled photon pairs based on a silicon photonic crystal cavity, implemented in a fully CMOS-compatible platform. In this device, resonantly enhanced spontaneous four-wave mixing converts pump photon pairs into signal/idler photon pairs under the energy-conserving condition in the telecommunication C-band. The design of the resonator is based on an effective bichromatic confinement potential, allowing it to achieve up to nine close-to-equally spaced modes in frequency, while preserving small mode volumes, and the whole chip, including grating couplers and access waveguides, is fabricated in a single run on a silicon-on-insulator platform. Besides demonstrating efficient photon pair generation, we also implement a Franson-type interference experiment, demonstrating entanglement between signal and idler photons with a Bell inequality violation exceeding five standard deviations. The high generation efficiency combined with the small device footprint in a CMOS-compatible integrated structure opens a pathway toward the implementation of compact quantum light sources in all-silicon photonic platforms.

Exploring Bell inequalities and quantum entanglement in vector boson scattering

Exploring Bell inequalities and quantum entanglement in vector boson scattering

Experimentally Ruling Out Joint Reality Based on Locality with Device-Independent Steering

As an essential concept to understand the world, whether the real values (or physical realities) of observables are suitable to physical systems beyond the classic has been debated for many decades. Although standard no-go results based on Bell inequalities have ruled out the joint reality of incompatible quantum observables, the possibility of giving simple yet strong arguments to rule out joint reality in any physical system (not necessarily quantum) with weaker assumptions and less observables has been explored and proposed recently. Here, we perform a device-independent experiment on a two-qubit superconducting system to show that the joint reality of two observables is incompatible with locality under the weaker assumption of the reality of observables in a single space-time region (or single qubit). Our results clearly show the violation of certain inequalities derived from both linear and nonlinear criteria. In addition, we study the robustness of the linear and nonlinear criterion against the effect of systematic decoherence. Our demonstration opens up the possibility of delineating classical and non-classical boundaries with simpler nontrivial quantum system.

Certification of non-Gaussian Einstein–Podolsky–Rosen steering

Non-Gaussian quantum states are a known necessary resource for reaching a quantum advantage and for violating Bell inequalities in continuous variable systems. As one kind of manifestation of quantum correlations, Einstein–Podolsky–Rosen steering enables verification of shared entanglement even when one of the subsystems is not characterized. However, how to detect and classify such an effect for non-Gaussian states is far from being well understood. Here, we present an efficient non-Gaussian steering criterion based on the high-order observables and conduct a systematic investigation into the hierarchy of non-Gaussian steering criteria. Moreover, we apply our criterion to three experimentally-relevant non-Gaussian states under realistic conditions and, in particular, propose a feasible scheme to create multi-component cat states with tunable size by performing a suitable high-order quadrature measurement on the steering party. Our work reveals the fundamental characteristics of non-Gaussianity and quantum correlations, and offers new insights to explore their applications in quantum information processing.

Hardy-Bell inequalities and fault-tolerant Hardy paradoxes

Usually, the verification of Bell nonlocality involves two main approaches: violation of specific inequalities and utilization of no-inequality methods. In this paper, we continue to develop the inequality methods by deducing the so-called ‘Hardy-Bell inequalities (HBIs)’ and ‘fault-tolerant Hardy paradoxes (FTHPs)’ for correlation tensors (CTs) with two inputs and general outcomes. We prove that the HBIs are necessary conditions for a CT to be Bell local and one of the FTHPs is sufficient condition for a CT to be Bell nonlocal. We demonstrate the effectiveness of HBIs in determining the nonlocality of CTs or quantum states when the classical Hardy paradox does not appear or a Bell inequality is not violated. Consequently, our methods can be utilized to explore more correlations having Bell nonlocality. Based on the obtained results, we find a neighborhood of a Hardy nonlocal state, in which all states are all Bell nonlocal.

Violation of Bell’s inequality for helical Mathieu–Gauss vector modes

Vector beams display varying polarisation over planes transversal to their direction of propagation. The variation of polarisation implies that the electric field cannot be expressed as a product of a spatial mode and its polarisation. This non-separability has been analysed for particular vector beams in terms of non–quantum entanglement between the spatial and the polarisation-degrees of freedom, and equivalently, with respect to the degree of polarisation of light. Here we demonstrate theoretically and experimentally that Mathieu–Gauss vector modes violate a Bell-like inequality known as the Clauser–Horn–Shimony–Holt–Bell inequality. This demonstration provides new insights on the violation of Bell inequalities by a more general class of vector modes with elliptical symmetry.

Heterodox underdetermination: Metaphysical options for discernibility and (non-)entanglement

Broadly speaking, there are three views on whether Leibniz's Principle of the Identity of Indiscernibles (PII) is violated in the case of similar particles. According to the earliest view, PII is always violated (call this the no discernibility view); according to the more recent weak discernibility view, PII is at least valid in a weak sense. No and weak discernibility have been referred to as orthodoxy. Steven French has argued that although PII is violated, similar particles can still be regarded as individuals, or, alternatively, as non-individuals: French famously concluded therefore that metaphysics is underdetermined by physics. Call this thesis orthodox underdetermination. Most recently, some authors have turned against orthodoxy by arguing that PII is valid in more than a weak sense – call this the new discernibility view, also referred to as heterodoxy. Since heterodoxy is backed up by physical considerations, metaphysics now seems to be determined by physics: physics indicates that PII is valid. In this paper, I argue that with respect to entangled states, there are two ways to establish PII's validity, which yield two different ontological interpretations of entanglement. Therefore, a form of underdetermination returns within the heterodox framework. I argue that heterodox underdetermination deserves some attention, because the two ontological interpretations might yield different explanations of the violation of Bell inequalities.

Generalized iterative formula for Bell inequalities

Generalized iterative formula for Bell inequalities

Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.