Violation Of Inequality Research Articles

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

Fast simulation for multi-photon, atomic-ensemble quantum model of linear optical systems addressing the curse of dimensionality

Photons are elementary particles of light in quantum mechanics, whose dynamics can be difficult to gain detailed insights, especially in complex systems. Simulation is a promising tool to resolve this issue, but it must address the curse of dimensionality, namely, that the number of bases increases exponentially in the number of photons. Here we mitigate this dimensionality scaling by focusing on optical systems composed of linear optical objects, modeled as an ensemble of two-level atoms. We decompose the time evolutionary operator on multiple photons into a group of time evolution operators acting on a single photon. Since the dimension of a single-photon time evolution operator is exponentially smaller than that of a multi-photon one in the number of photons, the decomposition enables the multi-photon simulations to be performed at a much lower computational cost. We apply this method to basic single- and multi-photon phenomena, such as Hong–Ou–Mandel interference and violation of the Bell-CHSH inequality, and confirm that the calculated properties are quantitatively comparable to the experimental results. Furthermore, our method visualizes the spatial propagation of photons hence provides insights that aid experiment designs for quantum-enabled technologies.

Single-Shot Readout of a Solid-State Electron Spin Qutrit.

Quantum systems usually feature a rich multilevel structure with promising resources for developing superior quantum technologies compared with their binary counterpart. Single-shot readout of these high-dimensional quantum systems is essential for exploiting their potential. Although there have been various high-spin systems, the single-shot readout of the overall state of high-spin systems remains a challenging issue. Here we demonstrate a reliable single-shot readout of spin qutrit state in a low-temperature solid-state system utilizing a binary readout scheme. We achieve a single-shot readout of an electron spin qutrit associated with a single nitrogen-vacancy center in diamond with an average fidelity of 87.80%. We use this spin qutrit system to verify quantum contextuality, a fundamental test of quantum mechanics. We observe a violation of the noncontextual hidden variable inequality with the developed single-shot readout in contrast to the conventional binary readout. These results pave the way for developing quantum information processing based on spin qutrits.

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.

Generalization of Gisin’s theorem to quantum fields

We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.

Experimentally ruling out joint reality based on operational completeness

Whether the observables of a physical system admit real values is of fundamental importance to a deep understanding of nature. In this work, we report a device-independent experiment to confirm that the joint reality of two observables on a single two-level system is incompatible with the assumption of operational completeness, which is strictly weaker than that of preparation noncontextuality. We implement two observables on a trapped 171Yb+ ion to test this incompatibility via violation of certain inequalities derived from both linear and nonlinear criteria. Moreover, by introducing a highly controllable dephasing channel, we show that the nonlinear criterion is more robust against noise. Our results push the fundamental limit to delineate the quantum–classical boundary and pave the way for exploring relevant problems in other scenarios.

A Study of Triangle Inequality Violations in Social Network Clustering

A Study of Triangle Inequality Violations in Social Network Clustering

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.

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.

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.

A Macroscopic Quantum Three-Box Paradox: Finding Consistency with Weak Macroscopic Realism.

The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening box 3. The paradox is that the ball would have been found with certainty by Bob in either box if that box had been opened. Resolutions of the paradox include that Bob's measurement cannot be made non-invasively or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes prior to Bob or Alice opening any boxes. We demonstrate the consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any boxes but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: the paradox only manifests if Alice's shuffling combines both local operations (on box 3) and nonlocal operations, on the other boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett-Garg inequality, which implies failure of non-invasive measurability if wMR holds.

Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios

We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens existing arguments regarding robustness of experimental implementations. As a case study, we demonstrate quantum contextuality associated with any nontrivial noncontextuality inequality for a class of useful scenarios by noticing a connection between the resource theory and measurement simulability. Additionally, we expose a formal composition rule that allows engineering complex scenarios from simpler ones. This approach provides insights into the noncontextual polytope structure for complex scenarios and facilitates the identification of possible quantum violations of noncontextuality inequalities.

Exploring the impact of spontaneous emission in two quantum game-based key-distribution protocols

In this work, we investigate the influence that spontaneous emission has on the performance and security of both a qubit and a qutrit quantum key distribution protocols, if these were to be implemented using two- and three-level atoms, respectively. These protocols were developed based on the mechanics of a quantum version of the Monty-Hall game. In the case of three-level atoms, the three possible configurations (V, Ξ, Λ) are considered. In both protocols, an additional step, consisting on discarding some specific non-valid cases, is found to reduce the bit error ratio (BER). Regarding the security of the protocols, we are able to define secure regions, dependent on the spontaneous emission parameters, within which the protocols are deemed secure due to the violation of Bell-type inequalities. Furthermore, our results show that the choice of three-level atom configuration significantly impacts the protocol performance. We are able to determine that the Λ configuration provides a lower BER than the V and Ξ configurations within their respective secure regions.

BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson’s bound. An illustrative comparison with the entangled state of two 1/21/2 spin particles in Quantum Mechanics is provided.

Nonclassical magnon pair generation and Cauchy-Schwarz inequality violation

Nonclassical magnon pair generation and Cauchy-Schwarz inequality violation

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.

Entanglement and Bell inequalities violation in Hrightarrow ZZ with anomalous coupling

We discuss entanglement and violation of Bell-type inequalities for a system of two Z bosons produced in Higgs decays. We take into account beyond the Standard Model (anomalous) coupling between H and daughter bosons but we limit ourselves to an overall scalar ZZ state (we exclude the possibility that H contains a pseudo-scalar component). In particular we consider the case when each Z decays further into fermion-antifermion pair. We find that the ZZ state is entangled and violates the CGLMP inequality for all values of the (anomalous) coupling constant. We also discuss the impact of a background on these results. The methods we develop are completely general, since they can be extrapolated to any scalar particle decaying into two spin-1 particles of different masses. Moreover, the violation of the CGLMP inequality in the final state is theoretically ensured for any value of the couplings.

Weyl operators, Tomita-Takesaki theory, and Bell-Clauser-Horne-Shimony-Holt inequality violations

Weyl operators, Tomita-Takesaki theory, and Bell-Clauser-Horne-Shimony-Holt inequality violations

Exploring causality in braneworld/cutoff holography via holographic scattering

Holography with branes and/or cutoff surfaces presents a promising approach to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes. However, this generalized holography is known to face several inconsistencies, including potential violations of causality and fundamental entropic inequalities. In this work, we address these challenges by investigating the bulk scattering process and its holographic realization. Specifically, we propose that the information on a brane/cutoff surface Q propagates according to the induced light cones originating from a fictitious asymptotic boundary behind Q, rather than the conventional ones originating from a point on Q. Additionally, we establish the validity of the connected wedge theorem for generalized holography with induced light cones. We also demonstrate that entropic inequalities remain valid within the induced causal diamonds. While the induced light cone seemingly permits superluminal signaling, we argue that this causality violation can be an artifact of state preparation for radially propagating excitations, rather than local operator excitations on Q.