Nonlocality Of Quantum Mechanics Research Articles

Quantum Entanglement and Nonlocality: Challenging the Local Realism of Classical Physics

Abstract. This paper delves into the significance and impact of quantum entanglement across the fields of physics, information science, and philosophy. Utilizing a literature review approach, the paper first introduces the concept and historical background of quantum entanglement, emphasizing its challenge to the limitations of classical physics and its potential applications in quantum communication and quantum computing. This paper thoroughly explains the theoretical foundations of the Einstein-Podolsky-Rosen experiment and Bell's inequality, along with related experimental validations and key results. In particular, it elucidates how quantum entanglement reveals the nonlocality in quantum mechanics and the characteristics of nonlocal information transfer. The discussion then shifts to the challenge quantum entanglement poses to physical ontology, exploring the philosophical implications and the new perspectives it offers in information theory. Finally, this study concludes by summarizing the profound impact of quantum entanglement as one of the most challenging and inspiring research areas in contemporary physics on scientific theory and philosophical thought, as well as anticipating future research directions and potential applications.

Quantum entanglement: Principles and research progress in quantum information processing

Quantum entanglement is a peculiar phenomenon in quantum information science, characterized by nonclassical correlations between quantum states of subsystems in a quantum system. Since the proposal of the Einstein-Podolsky-Rosen (EPR) paradox by Einstein, Podolsky, and Rosen, quantum entanglement has sparked intense debates on local realism. Bells inequality experiment established the nonlocality of quantum mechanics. Currently, high-dimensional quantum entanglement of both deterministic and random states can be realized in systems such as photons and cold atoms. Technologies such as quantum teleportation, quantum teleportation, quantum computing, and others rely on quantum entanglement to achieve effects beyond classical limitations. Current research focuses on the implementation of macroscopic quantum entanglement and its significance in fundamental problems of quantum mechanics. Quantum entanglement opens up a new paradigm for information processing with broad application prospects. It is necessary to conduct in-depth research on the nature of quantum entanglement and its advantages in information processing. This paper reviews the theoretical foundations of quantum entanglement, methods of generation and detection, and research progress in its applications in the field of quantum information. It discusses the important applications of quantum entanglement in quantum communication, computing, and sensing and provides an outlook on the future development prospects of quantum entanglement technologies.

An effective way of characterizing the quantum nonlocality

Nonlocality is a distinctive feature of quantum theory, which has been extensively studied for decades. It is found that the uncertainty principle determines the nonlocality of quantum mechanics. Here we show that various degrees of nonlocalities in correlated system can be characterized by the generalized uncertainty principle, by which the complementarity is attributed to the mutual dependence of observables. Concrete examples for different kinds of nonclassical phenomena pertaining to different orders of dependence are presented. We obtain the third-order “skewness nonlocality” and find that the Bell nonlocality turns out to be merely the second-order “variance nonlocality” and the fourth-order dependence contains the commutator squares, which hence is related to the quantum contextuality. More applications of the generalized uncertainty principle are expected.

On Quantum Causality

For Kant causality is an a priori category of the understanding, a necessary condition for the possibility of any experience. Later Wittgenstein’s philosophy rejects transcendentalism. We can only speak of causes and effects if in some basic situations, or ‘language games’, we already treat some things as causes of what happens. Since the notion of cause becomes meaningful only within a language game, it is not unambiguous. Quantum causal language games presuppose the use of quantum theory. We treat the latter as Wittgenstein’s grammar of a quantum form of life’, or rule (norm), anchored in its applications — quantum phenomena as language games. Quantum correlations are often interpreted as a manifestation of the nonlocality of quantum mechanics. This is a view of quantum phenomena from the perspective of classical physics. Our contextual point of view rejects the nonlocality of quantum theory in the sense of instantaneous causal influence at a distance. But it does not admit its locality in the sense of classical causality either. We introduce the notion of quantum causality which allows us to treat quantum correlations as local, but context-dependent. Their formal cause is an entangled wave function. Any particular quantum correlation, identifiable in a context of its observation as a result of the wave function reduction, post factum can be treated as a classical causal correlation. From the point of view of the proposed contextual quantum realism, epistemology is secondary, and ontology is sensitive to context. Quantum correlations exist (are real) before application of the theory, independently of their identification (description, measurement), but have no identity, which appears only as a result of application of the theory and their identification in the context. In other words, they are real, but not pre-determined, not autonomous.

STRONGLY VIOLATED SCALE INVARIANCE OF SPACE-TIME (QUANTUM-MECHANICAL ASPECT)

The hypothesis that the Universe in its evolution exhibits, to one degree or another, strongly violated scale invarianceis discussed. The fundamental group of space-time now is not the Poincaré group, but the Poincaré-Weyl group. In case with a very high probability a particle is found near its classical trajectory, but there is an extremely small (but nonetheless nonzero!) probability of detecting this particle far from its classical trajectory, providing quantum mechanical nonlocality both in space and in time. The considerations presented here, in their further study, may lead to the formulation of a new interpretation of quantum mechanics. А possible change in Planck’s constant over time is discussed.

Quantization of nonlocal fields via fractional calculus

In this study, we investigate the effect of nonlocality in quantum mechanics and propose a fractional approach the theory of quantized fields. For this purpose, we embedded the fractional calculus to broaden theory of quantum fields since the integral and derivative operators are nonlocal in fractional calculus.Additionally, quantum entanglement is discussed to gain comprehension of nonlocality in the foundation of quantum mechanics. Besides, fractional Lagrangian formalism was presented due to fact that the Lagrangian density is the starting point to establish a field theory.Furthermore, to make fractional field operators quantum mechanical, equal-time commutator have been defined for the these operators in terms of Caputo fractional derivative. Thus, a scheme of quantization of fractional fields is introduced and general aspects of the method is illustrated with the theory of massive scalar fields. This approach laid out to a successful generalization of the quantum field theory which is coherent with the standard formalism. Consequently, we developed promising concept for a quantum field theory by introducing nonlocality into standard mathematical formalism.

There Is No Spooky Action at a Distance in Quantum Mechanics.

Einstein became bothered by quantum mechanical action at a distance within two years of Schrödinger’s introduction of his eponymous wave equation. If the wave function represents the “real” physical state of a particle, then the measurement of the particle’s position would result in the instantaneous collapse of the wave function to the single, measured position. Such a process seemingly violates not only the Schrödinger equation but also special relativity. Einstein was not alone in this vexation; however, the dilemma eventually faded as physicists concentrated on using the Schrödinger equation to solve a plethora of pressing problems. For the next 30 years, wave function collapse, while occasionally discussed by physicists, was primarily a topic of interest for philosophers. That is, until 1964, when Bell introduced his famous inequality and maintained that its violation proved that quantum mechanics and, by implication, nature herself are nonlocal. Unfortunately, this brought the topic back to mainstream physics, where it has remained and continues to muddy the waters. To be sure, not all physicists are bothered by the apparent nonlocality of quantum mechanics. So where have those who embrace quantum nonlocality gone wrong? I argue that the answer is a gratuitous belief in the ontic nature of the quantum state.

Estimation of the CHSH Parameter Using HOM Interference

The Clauser–Horne–Shimony–Holt (CHSH) experiment is an essential test of nonlocality in quantum mechanics and can be used to validate the principle of entanglement. In addition to verifying entanglement, the measurable CHSH parameter can also be used to gauge the quality of the entanglement present in a system. The measurement of Hong–Ou–Mandel (HOM) interference is another important fundamental experiment in quantum optics that measures the indistinguishability of a pair of photons. In this article, we demonstrate how the results of a HOM interference experiment, a relatively simple experiment, can be used to obtain an estimate for the value of the CHSH <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> parameter, which is a more complicated measurement. We experimentally demonstrate that the HOM interference technique is capable of providing an estimate of the value of the CHSH parameter that is within one standard deviation of measurement error when spectral impairments are present. We expect that this technique will aid in the calibration of quantum optical systems.

Real-time ghost imaging of Bell-nonlocal entanglement between a photon and a quantum memory

Certification of nonlocality of quantum mechanics is an important fundamental test that typically requires prolonged data collection and is only revealed in an in-depth analysis. These features are often particularly exposed in hybrid systems, such as interfaces between light and atomic ensembles. Certification of entanglement from images acquired with single-photon camera can mitigate this issue by exploiting multiplexed photon generation. Here we demonstrate this feature in a quantum memory (QM) operating in a real-time feedback mode. Through spatially-multimode spin-wave storage the QM enables operation of the real-time ghost imaging (GI) protocol. By properly preparing the spatial phase of light emitted by the atoms we enable observation of Bell-type nonlocality from a single image acquired in the far field as witnessed by the Bell parameter of S=2.227±0.007&gt;2. Our results are an important step towards fast and efficient utilization of multimode quantum memories both in protocols and in fundamental tests.

Information Causality without Concatenation.

Information causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonlocality of quantum mechanics without resorting to its full formalism, with a notable example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. Despite being promising, the latter result found little generalization to other Bell inequalities because of the limitations imposed by the process of concatenation, in which several nonsignaling resources are put together to produce tighter bounds. In this work, we show that concatenation can be successfully replaced by limits on the communication channel capacity. It allows us to rederive and, in some cases, significantly improve all the previously known results in a simpler manner and apply the information causality principle to previously unapproachable Bell scenarios.

Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.

The measurement problem in Quantum Mechanics: Convivial Solipsism

The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve (or to dissolve) it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. In this paper, I defend a new position, the “Convivial Solipsism”, according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett’s interpretation and sharing also some similarities with Rovelli’s relational interpretation and Quantum Bayesianism. I also show how “Convivial Solipsism” can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics.

Geometrical hypotheses underlying wave functions and their emerging dynamics

Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being configuration space. The target space is argued to be 2-dimensional and flat, and their orthogonal directions are physically interpreted. All terms in the map equation have a geometrical meaning in the target space, and the pull-back of its rotational Killing one-form allows the construction of a velocity field in configuration space. Identification of this velocity field with tangent vectors in the source space leads to the dynamical law of motion. For a specific choice of an arbitrary scalar function present in the map equation, and using Cartesian coordinates in the target space, the map equation becomes linear and can be reduced to the Schr\"odinger equation. We link the bi-dimensionality of the target space with the essential non-locality of quantum mechanics. Many extensions of the framework here presented are immediate, with deep consequences yet to be explored.

Manifest non-locality in quantum mechanics, quantum field theory and quantum gravity

We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

Cosmological horizons, uncertainty principle, and maximum length quantum mechanics

The cosmological particle horizon is the maximum measurable length in the Universe. The existence of such a maximum observable length scale implies a modification of the quantum uncertainty principle. Thus due to non-locality of quantum mechanics, the global properties of the Universe could produce a signature on the behaviour of local quantum systems. A Generalized Uncertainty Principle (GUP) that is consistent with the existence of such a maximum observable length scale $l_{max}$ is $\Delta x \Delta p \geq \frac{\hbar}{2}\;\frac{1}{1-\alpha \Delta x^2}$ where $\alpha = l_{max}^{-2}\simeq (H_0/c)^2$ ($H_0$ is the Hubble parameter and $c$ is the speed of light). In addition to the existence of a maximum measurable length $l_{max}=\frac{1}{\sqrt \alpha}$, this form of GUP implies also the existence of a minimum measurable momentum $p_{min}=\frac{3 \sqrt{3}}{4}\hbar \sqrt{\alpha}$. Using appropriate representation of the position and momentum quantum operators we show that the spectrum of the one dimensional harmonic oscillator becomes $\bar{\mathcal{E}}_n=2n+1+\lambda_n \bar{\alpha}$ where $\bar{\mathcal{E}}_n\equiv 2E_n/\hbar \omega$ is the dimensionless properly normalized $n^{th}$ energy level, $\bar{\alpha}$ is a dimensionless parameter with $\bar{\alpha}\equiv \alpha \hbar/m \omega$ and $\lambda_n\sim n^2$ for $n\gg 1$ (we show the full form of $\lambda_n$ in the text). For a typical vibrating diatomic molecule and $l_{max}=c/H_0$ we find $\bar{\alpha}\sim 10^{-77}$ and therefore for such a system, this effect is beyond reach of current experiments. However, this effect could be more important in the early universe and could produce signatures in the primordial perturbation spectrum induced by quantum fluctuations of the inflaton field.

Quantum and superquantum enhancements to two-sender, two-receiver channels

We study the consequences of 'super-quantum non-local correlations' as represented by the PR-box model of Popescu and Rohrlich, and show PR-boxes can enhance the capacity of noisy interference channels between two senders and two receivers. PR-box correlations violate Bell/CHSH inequalities and are thus stronger -- more non-local -- than quantum mechanics; yet weak enough to respect special relativity in prohibiting faster-than-light communication. Understanding their power will yield insight into the non-locality of quantum mechanics. We exhibit two proof-of-concept channels: first, we show a channel between two sender-receiver pairs where the senders are not allowed to communicate, for which a shared super-quantum bit (a PR-box) allows perfect communication. This feat is not achievable with the best classical (senders share no resources) or quantum entanglement-assisted (senders share entanglement) strategies. Second, we demonstrate a class of channels for which a tunable parameter achieves a double separation of capacities; for some range of \epsilon, the super-quantum assisted strategy does better than the entanglement-assisted strategy, which in turn does better than the classical one.

Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on local hidden variable models that define joint probabilities for noncommuting observables. We find Quasi-Bell inequalities have a quantum to classical violation as high as $\frac{3}{2}$, higher than conventional Bell inequalities. The result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics, and provides an insightful generalization of Bell inequalities.

Quantum Mechanics in a New Light

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata (measurement outcomes), and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman's formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue--eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations.

Survey on nonlocal games and operator space theory

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

Investigation of quantum-entanglement simulation in random-variable theories augmented by either classical communication or nonlocal effects

Bell's theorem states that quantum mechanics is not a locally causal theory. This state is often interpreted as nonlocality in quantum mechanics. Toner and Bacon [Phys. Rev. Lett. \textbf{91}, 187904 (2003)] have shown that a shared random-variables theory augmented by one bit of classical communication exactly simulates the Bell correlation in a singlet state. In this paper, we show that in Toner and Bacon protocol, one of the parties (Bob) can deduce another party's (Alice) measurement outputs, if she only informs Bob of one of her own outputs. Afterwards, we suggest a nonlocal version of Toner and Bacon protocol wherein classical communications is replaced by nonlocal effects, so that Alice's measurements cause instantaneous effects on Bob's outputs. In the nonlocal version of Toner and Bacon's protocol, we get the same result again. We also demonstrate that the same approach is applicable to Svozil's protocol.