Violation Of Bell Research Articles

Unmasking the polygamous nature of quantum nonlocality

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality, then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signaling principle, and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here, we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements, and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of [Formula: see text] observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.

Quantum Entanglement between Optical and Microwave Photonic Qubits

Entanglement is an extraordinary feature of quantum mechanics. Sources of entangled optical photons were essential to test the foundations of quantum physics through violations of Bell’s inequalities. More recently, entangled many-body states have been realized via strong nonlinear interactions in microwave circuits with superconducting qubits. Here, we demonstrate a chip-scale source of entangled optical and microwave photonic qubits. Our device platform integrates a piezo-optomechanical transducer with a superconducting resonator which is robust under optical illumination. We drive a photon-pair generation process and employ a dual-rail encoding intrinsic to our system to prepare entangled states of microwave and optical photons. We place a lower bound on the fidelity of the entangled state by measuring microwave and optical photons in two orthogonal bases. This entanglement source can directly interface telecom wavelength time-bin qubits and gigahertz frequency superconducting qubits, two well-established platforms for quantum communication and computation, respectively. Published by the American Physical Society 2024

Entropy Bounds for Device-Independent Quantum Key Distribution with Local Bell Test.

One of the main challenges in device-independent quantum key distribution (DIQKD) is achieving the required Bell violation over long distances, as the channel losses result in low overall detection efficiencies. Recent works have explored the concept of certifying nonlocal correlations over extended distances through the use of a local Bell test. Here, an additional quantum device is placed in close proximity to one party, using short-distance correlations to verify nonlocal behavior at long distances. However, existing works have either not resolved the question of DIQKD security against active attackers in this setup, or used methods that do not yield tight bounds on the key rates. In this work, we introduce a general formulation of the key rate computation task in this setup that can be combined with recently developed methods for analyzing standard DIQKD. Using this method, we show that if the short-distance devices exhibit sufficiently high detection efficiencies, positive key rates can be achieved in the long-distance branch with lower detection efficiencies as compared to standard DIQKD setups. This highlights the potential for improved performance of DIQKD over extended distances in scenarios where short-distance correlations are leveraged to validate quantum correlations.

Fully controllable time-bin entangled states distributed over 100-km single-mode fibers

Quantum networks that can perform user-defined protocols beyond quantum key distribution will require fully controllable entangled quantum states. To expand the available space of generated time-bin entangled states, we demonstrate a time-bin entangled photon source that produces qubit states |ψ〉=α|00〉+β|11〉\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|{\\psi}\\rangle = \\alpha |{00}\\rangle + \\beta |{11}\\rangle $\\end{document} with fully controllable phase and amplitudes. Eight different two-photon states have been selected and prepared from arbitrary states on the reduced two-qubit Bloch sphere. The photon pairs encoded in the time-bin scheme were generated at 2.4 MHz with a visibility of V=0.9475±0.0016\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$V = 0.9475 \\pm 0.0016$\\end{document}, with a violation of the CHSH Bell’s inequality by 197 standard deviations. After entanglement distribution over 100 km of single-mode fibers, we obtained a visibility of V=0.9541±0.0113\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$V = 0.9541 \\pm 0.0113$\\end{document} with a violation of the CHSH Bell’s inequality by 6 standard deviations. The prepared states had an average fidelity of 0.9540±0.0016\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$0.9540 \\pm 0.0016$\\end{document} at the source and an average fidelity of 0.9353−0.0209+0.0100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$0.9353 ^{+0.0100}_{-0.0209}$\\end{document} after entanglement distribution, which shows that the quantum states generated by our time-bin entangled photon source can be fully controlled potentially to a level applicable to long-distance advanced quantum network systems.

EPR Correlations Using Quaternion Spin

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 12—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 12, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox.

Nonclassicality and teleportation fidelity probes in amplitude-tailored superconducting charge qubits

Optimal procedures and appropriate designs of transmitting channels are required to preserve quantum correlations (QCs) in quantum teleportation schemes. In pursuit of this objective, a comprehensive investigation into the intricate dynamics of a quantum channel comprising two singular Cooper-pair charge qubits, mutually coupled and influenced by Josephson energy, has been undertaken. The use of the Gibbs density operator has provided valuable insights into the thermal quantum characteristics and teleportation fidelity of the system. Furthermore, this study underscores the critical interplay between the energy parameters and the utilization of quantum features to establish conducive conditions for the preservation of nonclassicality and the success of the teleportation scheme. Additionally, the study reveals that trace distance discord is the most resilient in the thermal output state, surpassing both concurrence and the degree of violation of Bell’s inequality. Notably, precise control of the input state amplitude and adept manipulation of the energy parameters have enhanced QCs and resulted in the teleportation fidelity exceeding the classical limit.

Optimizing fictitious states for Bell inequality violation in bipartite qubit systems with applications to the tt¯ system

There is a significant interest in testing quantum entanglement and Bell inequality violation in high-energy experiments. Since the analyses in high-energy experiments are performed with events statistically averaged over phase space, the states used to determine observables depend on the choice of coordinates through an event-dependent basis and are thus not genuine quantum states, but rather “fictitious states.” We find that the basis which diagonalizes the spin-spin correlations is optimal for constructing fictitious states to test the violation of Bell’s inequality. This result is applied directly to the bipartite qubit system of a top and antitop produced at a hadron collider. We show that the beam axis is the optimal basis choice near the tt¯ threshold production for measuring Bell inequality violation, while at high transverse momentum the basis that aligns along the momentum direction of the top is optimal. Published by the American Physical Society 2024

Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases

The effects of Aharonov–Casher (AC) and He–McKellar–Wilkens (HMW) phases on entangled spin-1/2 quantum systems are investigated. We use linear charge distributions positioned at the center of resulting closed orbits, capitalizing on Mach Zender-type interferometers modified with phase retarders to unveil the topological effects. We analyze how AC-HMW phases influence the Bell angles and maximal violation of Bell–CHSH inequalities (BI) without any classical interaction. We incorporate the spin and path of particles in the interferometers as observables to test noncontextual hidden variable theories against quantum mechanics, leveraging the non-local features of AC-HMW effects. Furthermore, we discuss potential implementations of our scheme in physical systems.

Certifying long-range quantum correlations through routed Bell tests

Losses in the transmission channel, which increase with distance, pose a major obstacle to photonics demonstrations of quantum nonlocality and its applications. Recently, Chaturvedi, Viola, and Pawlowski (CVP) [arXiv:2211.14231] introduced a variation of standard Bell experiments with the goal of extending the range over which quantum nonlocality can be demonstrated. These experiments, which we call `routed Bell experiments', involve two distant parties, Alice and Bob, and allow Bob to route his quantum particle along two possible paths and measure it at two distinct locations – one near and another far from the source. The premise is that a high-quality Bell violation in the short-path should constrain the possible strategies underlying the experiment, thereby weakening the conditions required to detect nonlocal correlations in the long-path. Building on this idea, CVP showed that there are certain quantum correlations in routed Bell experiments such that the outcomes of the remote measurement device cannot be classically predetermined, even when its detection efficiency is arbitrarily low. In this paper, we show that the correlations considered by CVP, though they cannot be classically predetermined, do not require the transmission of quantum systems to the remote measurement device. This leads us to define and formalize the concept of `short-range' and `long-range' quantum correlations in routed Bell experiments. We show that these correlations can be characterized through standard semidefinite-programming hierarchies for non-commutative polynomial optimization. We then explore the conditions under which short-range quantum correlations can be ruled out and long-range quantum nonlocality can be certified in routed Bell experiments. We point out that there exist fundamental lower-bounds on the critical detection efficiency of the distant measurement device, implying that routed Bell experiments cannot demonstrate long-range quantum nonlocality at arbitrarily large distances. However, we do find that routed Bell experiments allow for reducing the detection efficiency threshold necessary to certify long-range quantum correlations. The improvements, though, are significantly smaller than those suggested by CVP's analysis.

Violation of Bell’s Inequality in the Clauser-Horne-Shimony-Holt Form with Entangled Quantum States Revisited

Violation of Bell’s Inequality in the Clauser-Horne-Shimony-Holt Form with Entangled Quantum States Revisited

Stern–Gerlach, EPRB and Bell Inequalities: An Analysis Using the Quantum Hamilton Equations of Stochastic Mechanics

The discussion of the recently derived quantum Hamilton equations for a spinning particle is extended to spin measurement in a Stern–Gerlach experiment. We show that this theory predicts a continuously changing orientation of the particles magnetic moment over the course of its motion across the Stern–Gerlach apparatus. The final measurement results agree with experiment and with predictions of the Pauli equation. Furthermore, the Einstein–Podolsky–Rosen–Bohm thought experiment is investigated, and the violation of Bells’s inequalities is reproduced within this stochastic mechanics approach. The origin of the violation of Bell’s inequalities is traced to the the non-local nature of the velocity fields for an entangled state in the stochastic formalism, which is a result of a non-separable probability distribution of the considered particles.

Hidden variables and Bell’s theorem: Local or not?

Bell’s inequality is an empirical constraint on theories with hidden variables, which Einstein, Podolsky and Rosen argued are needed to explain observed perfect correlations if keeping locality. One way to deal with the empirical violation of Bell’s inequality is by openly embracing nonlocality, in a theory like the pilot-wave theory. Nonetheless, recent proposals have revived the possibility that one can avoid nonlocality by resorting to superdeterministic theories. These are local hidden variables theories which violate statistical independence which is one assumption of Bell’s inequality. In this paper I compare and contrast these two hidden variable strategies: the pilot-wave theory and superdeterminism. I show that even if the former is nonlocal and the other is not, both are contextual. Nonetheless, in contrast with the pilot-wave theory, superdeterminist contextuality makes it impossible to test the theory (which therefore becomes unfalsifiable and unconfirmable) and renders the theory uninformative (measurement results tell us nothing about the system). It is questionable therefore whether a theory with these features is worth its costs.

Photonic entanglement during a zero-g flight

Quantum technologies have matured to the point that we can test fundamental quantum phenomena under extreme conditions. Specifically, entanglement, a cornerstone of modern quantum information theory, can be robustly produced and verified in various adverse environments. We take these tests further and implement a high-quality Bell experiment during a parabolic flight, transitioning from microgravity to hypergravity of 1.8 g while continuously observing Bell violation, with Bell-CHSH parameters between S=−2.6202 and −2.7323, an average of S¯=−2.680, and average standard deviation of ΔS¯=0.014. This violation is unaffected both by uniform and non-uniform acceleration. This experiment demonstrates the stability of current quantum communication platforms for space-based applications and adds an important reference point for testing the interplay of non-inertial motion and quantum information.

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.

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.

Whence Nonlocality? Removing Spooky Action-at-a-Distance from the de Broglie Bohm Pilot-Wave Theory Using a Time-Symmetric Version of the de Broglie Double Solution

In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry.

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.

Principle and state-of-art applications of quantum information

Al. Last year, the Nobel Prize in Physics was awarded to Alain Aspect, John F. Clauser and Anton Zeilinger for their experimental verification of the violation of Bell's inequality by quantum mechanics using entangled photons, which pioneered the science of quantum information; in the same year, the 28th Solvay Conference on Physics, with the theme "Quantum Information In the same year, the 28th Solvay Conference on Physics, with the theme of "Quantum Information Physics", reviewed the development of quantum information in the last decade and the future direction. It is clear that the world of physics is now focused on the subsequent progress of quantum mechanics. In this paper, I will introduce the background of quantum information and explain in detail, clearly and thoroughly, the basic theory of quantum information and its specific applications. By describing the two fundamental and most important properties of quantum information, quantum entanglement and quantum unclonable, quantum information will give the reader a comprehensive understanding of the significance and usefulness of quantum information. This paper aims to help physics students to build up their basic knowledge of quantum information by explaining the basic theory of quantum information and helping them to expand their knowledge of quantum information.

Numerical simulation of Gedanken experiments involving violations of Bell’s inequalities

Entanglement exhibits a unique property of quantum theory that is unseen in classical counterparts. The experimental confirmation of Bell’s inequalities has surprised many people and revived interest and debate regarding the exact nature of quantum theory, including the wave-particle duality. On the other hand, rapid advancements in computing technology in recent years have provided a new tool for investigating the nature of quantum theory. In this paper, numerical simulation is used to visualize the nonlocality implied in quantum entanglement. In particular, a Gedanken experiment of a discrete approximation of a continuous quantum space is provided, similar to the case of the dual nature of particle/wave in the double-slit experiment. The results are expected to provide a different angle for a deeper understanding of the mysterious nature of quantum correlations.

Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario

One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when they are obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. In this paper, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to provide lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. We compare experimental setups providing Bell violations close to the Tsirelson’s bound with lower rates of events, with setups having slightly worse levels of violation but higher event rates. Our results demonstrate the first experiment that certifies close to two bits of randomness from binary measurements of two parties. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation theorem and show its advantages compared to existing solutions.