Bell Inequality Tests Research Articles

Entanglement-preserving measurement of the Bell parameter on a single entangled pair

Abstract Bell inequalities represent one of the cornerstones of quantum foundations, and a fundamental tool for quantum technologies. Although a lot of effort was put in exploring and generalizing them, because of the wave function collapse it was deemed impossible to estimate the entire Bell parameter from one entangled pair, since this would involve measuring incompatible observables on the same quantum state. Conversely, here it is reported the first implementation of a new generation of Bell inequality tests, able to extract a Bell parameter value from each entangled pair and, at the same time, preserve the pair entanglement instead of destroying it. This is obtained by exploiting sequences of weak measurements, allowing incompatible observable measurements on a quantum state without collapsing its wave function. On the fundamental side, by removing the need to choose between different measurement bases our approach stretches the concept of counterfactual definiteness, since it allows measuring the entangled pair in all the bases needed for the Bell inequality test, intrinsically eliminating the issues connected with the otherwise not-chosen bases. On the practical side, after our Bell parameter measurement the entanglement within the pair remains (basically) unaltered, hence exploitable for other quantum-technology-related or foundational purposes.

Testing Bell inequality through at CEPC* *Tong Li is Supported by the National Natural Science Foundation of China (12375096, 12035008, 11975129), and "the Fundamental Research Funds for the Central Universities", Nankai University (63196013). Kai Ma was supported by the Natural Science Basic Research Program of Shaanxi Province, China (2023-JC-YB-041) and the Innovation Capability Support Program of Shaanxi Province, China (2021KJXX-47)

The decay of Higgs boson into two spin-1/2 particles provides an ideal system to reveal quantum entanglement and Bell-nonlocality. Future colliders can improve the measurement accuracy of the spin correlation of tau lepton pairs from Higgs boson decay. We show the testability of Bell inequality through at Circular Electron Positron Collider (CEPC). Two realistic methods of testing Bell inequality are investigated, i.e., Törnqvist's method and Clauser-Home-Shimony-Holt (CHSH) inequality. In the simulation, we consider the detector effects of CEPC including uncertainties for tracks and jets from Z boson in the production of . Necessary reconstruction approaches are described to measure quantum entanglement between and . Finally, we show the sensitivity of CEPC to Bell inequality violation for the two methods.

CHSH Bell tests for optical hybrid entanglement

Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.

Graph-theoretic approach to Bell experiments with low detection efficiency

Bell inequality tests where the detection efficiency is below a certain threshold ηcrit can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low ηcrit and relatively low dimension d of the local quantum systems. The method has two steps. First, we show a family of bipartite Bell inequalities for which, for correlations produced by maximally entangled states, ηcrit can be upper bounded by a function of some invariants of graphs, and use it to identify correlations that require small ηcrit. We present examples in which, for maximally entangled states, ηcrit≤0.516 for d=16, ηcrit≤0.407 for d=28, and ηcrit≤0.326 for d=32. We also show evidence that the upper bound for ηcrit can be lowered down to 0.415 for d=16 and present a method to make the upper bound of ηcrit arbitrarily small by increasing the dimension and the number of settings. All these upper bounds for ηcrit are valid (as it is the case in the literature) assuming no noise. The second step is based on the observation that, using the initial state and measurement settings identified in the first step, we can construct Bell inequalities with smaller ηcrit and better noise robustness. For that, we use a modified version of Gilbert's algorithm that takes advantage of the automorphisms of the graphs used in the first step. We illustrate its power by explicitly developing an example in which ηcrit is 12.38% lower and the required visibility is 14.62% lower than the upper bounds obtained in the first step. The tools presented here may allow for developing high-dimensional loophole-free Bell tests and loophole-free Bell nonlocality over long distances.

Entanglement of Nambu Spinors and Bell Inequality Test without Beam Splitters.

The identification of electronic entanglement in solids remains elusive so far, which is owed to the difficulty of implementing spinor-selective beam splitters with tunable polarization direction. Here, we propose to overcome this obstacle by producing and detecting a particular type of entanglement encoded in the Nambu spinor or electron-hole components of quasiparticles excited in quantum Hall edge states. Because of the opposite charge of electrons and holes, the detection of the Nambu spinor translates into a charge-current measurement, which eliminates the need for beam splitters and assures a high detection rate. Conveniently, the spinor correlation function at fixed effective polarizations derives from a single current-noise measurement, with the polarization directions of the detector easily adjusted by coupling the edge states to a voltage gate and a superconductor, both having been realized in experiments. We show that the violation of Bell inequality occurs in a large parameter region. Our Letter opens a new route for probing quasiparticle entanglement in solid-state physics exempt from traditional beam splitters.

Quantum tops at the LHC: from entanglement to Bell inequalities

We present the prospects of detecting quantum entanglement and the violation of Bell inequalities in tbar{t} events at the LHC. We introduce a unique set of observables suitable for both measurements, and then perform the corresponding analyses using simulated events in the dilepton final state, reconstructing up to the unfolded level. We find that entanglement can be established at better than 5 sigma both at threshold as well as at high p_T already in the LHC Run 2 dataset. On the other hand, only very high-p_T events are sensitive to a violation of Bell inequalities, making it significantly harder to observe experimentally. By employing a sensitive and robust observable, two different unfolding methods and independent statistical approaches, we conclude that, at variance with previous estimates, testing Bell inequalities will be challenging even in the high luminosity LHC run.

Testing Bell inequalities in Higgs boson decays

Higgs boson decays produce pairs of W bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the W± pair may be reconstructed experimentally from the directions of the charged lepton decay products, and from it the expectation values of various Bell operators determined. Numerical simulations of H→WW⁎ decays indicate that violation of a generalised CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated. Experimental Bell tests could be performed at a variety of colliders and in different production channels. If reconstruction effects and backgrounds can be controlled then statistically significant violations could be observable even with datasets comparable to those already collected at the LHC.

Broadband-laser-diode pumped periodically poled potassium titanyl phosphate-Sagnac polarization-entangled photon source

We experimentally demonstrate a polarization-entangled photon source at 810 nm using a type-II phase-matched periodically poled potassium titanyl phosphate (PPKTP) crystal pumped by a low-cost, broadband laser diode with a central wavelength of 405 nm and a typical bandwidth of 0.53 nm. The PPKTP crystal is placed in a Sagnac loop to realize the compact size and high stability. The downconverted biphotons, the signal and the idler, have typical bandwidths of 5.57 and 7.32 nm. We prepare two Bell states | Ψ + ⟩ and | Ψ − ⟩ with the fidelities of 0.948 ± 0.004 and 0.963 ± 0.002 . In the polarization correlation measurement, the visibilities are all higher than 96.2%, and in the Bell inequality test, the S value can achieve 2.78 ± 0.01 . This high-quality and low-cost entangled photon source may have many practical applications in quantum information processing.

Testing Bell Inequalities at the LHC with Top-Quark Pairs.

Correlations between the spins of top-quark pairs produced at a collider can be used to probe quantum entanglement at energies never explored so far. We show how the measurement of a single observable can provide a test of the violation of a Bell inequality at the 98%C.L. with the statistical uncertainty of the data already collected at the Large Hadron Collider, and at the 99.99%C.L. with the higher luminosity of the next run. Detector acceptance, efficiency, and migration effects are taken into account. The test relies on the spin correlations alone and does not require the determination of probabilities-in contrast to all other tests of Bell inequalities.

Nonlocality, Steering, and Quantum State Tomography in a Single Experiment.

We investigate whether paradigmatic measurements for quantum state tomography, namely mutually unbiased bases and symmetric informationally complete measurements, can be employed to certify quantum correlations. For this purpose, we identify a simple and noise-robust correlation witness for entanglement detection, steering, and nonlocality that can be evaluated based on the outcome statistics obtained in the tomography experiment. This allows us to perform state tomography on entangled qutrits, a test of Einstein-Podolsky-Rosen steering and a Bell inequality test, all within a single experiment. We also investigate the trade-off between quantum correlations and subsets of tomographically complete measurements as well as the quantification of entanglement in the different scenarios. Finally, we perform a photonics experiment in which we demonstrate quantum correlations under these flexible assumptions, namely with both parties trusted, one party untrusted and both parties untrusted.

Loophole-free Bell test with multi-photon-subtracted two-mode squeezed state

We investigate the loophole-free Bell inequality test with a multi-photon-subtracted two-mode squeezed state (TMSS). The maximal loophole-free Bell inequality violation is S = 2.046 for bi-side single-photon-subtracted TMSS. We show that such a violation can be further improved to S = 2.070 for ideal bi-side five-photon subtractions. Such a result approaches Munro's optimal bound for loophole-free Bell inequality violation. We further develop a concise phase-space method for deriving the loophole-free Bell inequality violation, which enables us to obtain a series of numerical results for practical multi-photon subtraction with a beam splitter and photon detectors. Our results provide a physically implementable state for approaching Munro's optimal bound.

Polarization-Independent Coherent Spatial-Temporal Interface with Low Loss

A coherent interface between temporal and spatial degrees of freedom (DOFs) empowers photons to take advantage of both DOFs in quantum information processing. Such interfaces have either suffered from a typical loss of 1--3 dB or disturbed the polarization DOF in the conversion process. The authors realize a low-loss, polarization-independent, coherent interface between temporal and spatial DOFs (specifically time-bin and path modes), which promises applications like the postselection-loophole-free Bell inequality test, and can be put into a cavity to boost the generation rates of multiphoton polarization-entangled sources, or to enhance the scalability of sequential quantum metrology.

Non-invasive zero-delay time calibration of Hanbury-Brown and Twiss interferometers

Measuring photon autocorrelations via a Hanbury-Brown and Twiss (HBT) setup is a widely used experimental technique in quantum optics and is the base for quantum characterizations via Hong-Ou-Mandel interferometry, Bell inequality tests or quantum state tomography. The most common use for HBT measurements is the demonstration of single-photon emission from a quantum emitter. In order to make a definite statement and analyze the coincidence histograms obtained in the experiment, the temporal position of the zero delay time (ZDT) must be accurately known. In many cases, determining the ZDT requires tedious calibration measurements using light sources with known non-trivial photon correlations. Here we report on a non-invasive technique for measuring the ZDT in HBT setups based on avalanche photodiodes (APDs). The technique relies on the deliberate enhancement of optical crosstalk between the APDs. It can be used with any conventional laser source and therefore means a significant improvement for the easy calibration of the ZDT in HBT setups.

Clauser-Horne-Shimony-Holt Bell inequality test in an optomechanical device

We propose here a scheme, based on the measurement of quadrature phase coherence, aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate EPR-like correlations between the quadratures of the output fields of the two cavities, and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.

Testing Bell inequalities for multi-partite systems with frequency-encoded photonic qubits

Testing Bell inequalities for multi-partite systems with frequency-encoded photonic qubits

Contextuality without nonlocality in a superconducting quantum system.

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 models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Here we use a superconducting qutrit with deterministic, binary-outcome readouts to violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. This evidence of state-dependent contextuality also demonstrates the fitness of superconducting quantum circuits for fault-tolerant quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.

Tight Bound on Randomness for Violating the Clauser–Horne–Shimony–Holt Inequality

Free will (or randomness) has been studied to achieve loophole-free Bell's inequality test and to provide device-independent quantum key distribution security proofs. The required randomness such that a local hidden variable model (LHVM) can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality has been studied, but a tight bound has not been proved for a practical case that i) the device settings of the two parties in the Bell test are independent; and ii) the device settings of each party can be correlated or biased across different runs. Using some information theoretic techniques, we prove in this paper a tight bound on the required randomness for this case such that the CHSH inequality can be violated by certain LHVM. Our proof has a clear achievability and converse style. The achievability part is proved using type counting. To prove the converse part, we introduce a concept called profile for a set of binary sequences and study the properties of profiles. Our profile-based converse technique is also of independent interest.

Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres.

More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.

Demonstration of Quantum Nonlocality in the Presence of Measurement Dependence.

Quantum nonlocality stands as a resource for device independent quantum information processing (DIQIP), such as, for instance, device independent quantum key distribution. We investigate, experimentally, the assumption of limited measurement dependence, i.e., that the measurement settings used in Bell inequality tests or DIQIP are partially influenced by the source of entangled particle and/or by an adversary. Using a recently derived Bell-like inequality [G. Pütz, Phys. Rev. Lett. 113, 190402 (2014)] and a 99% fidelity source of partially entangled polarization photonic qubits, we obtain a clear violation of the inequality, excluding a much larger range of measurement dependent local models than would be possible with an adapted Clauser-Horne-Shimony-Holt (CHSH) inequality. It is therefore shown that the measurement independence assumption can be widely relaxed while still demonstrating quantum nonlocality.

Proposal for a motional-state Bell inequality test with ultracold atoms

We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell-state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-P representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to S~2.5 for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by S<2.