We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and quantum algorithm, implying nonlocal attacks of noise. We then argue that the quantum error correction method fails to protect quantum computation against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This shows that the implicit assumption of quantum error correction theory -- independence of noise and self-dynamics -- fails in long time regimes. We also use our approach to present {\it pure} decoherence and decoherence accompanied by dissipation in terms of spectral density of reservoir. The so-called {\it dynamical decoupling} method is discussed in this context. Finally, we propose {\it minimal decoherence model}, in which the only source of decoherence is vacuum. We optimize fidelity of quantum information processing under the trade-off between speed of gate and strength of decoherence.
Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirma…
An alternative description imbedding nonlocality in a relativistic chronology is proposed. It is argued that vindication of Quantum Mechanics in forthcoming experiments with moving beam-splitters would mean that there is no real time ordering behind the nonlocal correlations.
We demonstrate that the phenomenon known as Spontaneous Parametric Down Conversion is really an amplification, in a nonlinear crystal pumped by a laser, of certain pairs of modes of the electromagnetic zeropoint field. The demonstration is achieved by showing the existence of a related phenomenon, Spontaneous Parametric Up Conversion. This phenomenon, once observed, will cast doubt on the quantum-optical theory, which treats photons as the elementary objects of the light field. It will also lend greater credibility to the zeropoint-field description of optical entanglement phenomena. That desc…
We present a simple yet rigorous field theoretic demonstration of the nonlocality of a single-photon field. The formalism used allows us to calculate the electric field of a single-photon light beam sent through a beam splitter, which directly demonstrates that it is the light field, rather than the photon itself regarded as a particle, that exhibits nonlocality. Our results are obtained without using either inequalities or specific measurement apparatuses, so that they have perfectly general validity.
Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different concepts. Describing nonlocality by means of the maximal violation of two Bell inequalities, we study both entanglement and nonlocality for two and three spins in the XY model. Our results shed a new light into the description of nonlocality and the possible information-theoretic task limitations of entanglement in an infinite quantum system.
A problem with an instructive description of measurement process for sufficiently separated entangled quantum systems is well known. More precise and crafty experiments together with new technological challenges raise questions about sufficiency of formal use of "black-box" Copenhagen paradigm without subtleties of transition between quantum and classical worlds. In this work are discussed applications both standard interpretation of quantum mechanics and "unconventional" models, like relative state formulation, multiple clocks formalism, and extended probabilities.
Relativistic nonlocality (RNL) is a recently proposed relativistic nonlocal description which unifies relativity of simultaneity and superluminal nonlocality (without superluminal signaling). In this article RNL is applied to experiments with so-called 2 non-before impacts, leading to new rules of calculating the joint probabilities, and predictions conflicting with quantum mechanics. A real experiment using fast moving polarizing beam-splitters is proposed.
We review the long history of nonlocality in physics with special emphasis on the conceptual breakthroughs over the last few years. For the first time it is possible to study "nonlocality without signaling" {\it from the outside}, that is without all the quantum physics Hilbert space artillery. We emphasize that physics has always given a nonlocal description of Nature, except during a short 10 years gap. We note that the very concept of "nonlocality without signaling" is totally foreign to the spirit of relativity, the only strictly local theory.
An experiment demonstrating nonlocality at detection is proposed. A single-photon Michelson-Morley experiment could be performed under exactly the same conditions as well. Hence, the two experiments are "loophole free" to the same extent. It is argued that both quantum theory and relativity share the same experimental basis and derive from the same principles. Relativity and the quantum are two aspects of one and the same physical description of the world.
We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-loc…
Quantum nonlocality is revisited from a novel point of view by studying the problem of an originally classical particle immersed in the stochastic zero-point radiation field (zpf). The entire system is left to evolve until it reaches a state in which the radiative terms cancel each other in the mean in a first approximation. The ensuing approximate statistical description reduced to the particle's configuration space contains a nonclassical term due to the dispersion of the momentum, which depends on the density of particles ρ(x) and thus is nonlocal. This description is shown to be equivalent…
Bell nonlocality from compatibility of entanglement-breaking channels
Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）；Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University（国立成功大学物理系与量子前沿研究技术中心）；H. H. Wills Physics Laboratory, University of Bristol（布里斯托大学H.H.威尔斯物理实验室）；ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）
Investigation of near field of QED requires the refuse from an averaging of the Lorentz condition that smooths out some field peculiarities. Instead of it Schwinger decomposition of the 4-potential with the Bogoliubov method of interaction switching in time and in space regions is considered. At such approach near field is describable by the part of covariant Green function of QED, the fast-damping Schwinger function formed by longitudinal and scalar components of Aμ none restricted by light cone. This description reveals possibility of superluminal phenomena within the near field zone as…
We have applied an entanglement purification protocol to produce a single entangled pair of photons capable of violating a CHSH Bell inequality from two pairs that individually could not. The initial poorly-entangled photons were created by a controllable decoherence that introduced complex errors. All of the states were reconstructed using quantum state tomography which allowed for a quantitative description of the improvement of the state after purification.
We consider the reversible processes between two one-to-one correlated measurement outcomes which underly both problem-solving and quantum nonlocality. In the former case the two outcomes are the setting and the solution of the problem, in the latter those of measuring a pair of maximally entangled observables whose subsystems are space separate. We argue that the quantum description of these processes mathematically describes the correlation but leaves the causal structure that physically ensures it free, also of violating the time-symmetry required of the description of a reversible process.…
Recent work has argued that the concepts of entanglement and nonlocality must be taken seriously even in systems consisting of only a single particle. These treatments, however, are nonrelativistic and, if single particle entanglement is fundamental, it should also persist in a relativistic description. Here we consider a spin-1/2 particle in a superposition of two different velocities as viewed by an observer in a different relativistically-boosted inertial frame. We show that the entanglement survives right up to the speed of light and that the boosted observer would see single-particle viol…
Quantum Mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and interpretation. Herein, we analyze carefully the possible mathematical meanings of those terms used in analysis of EPR's contention, that Quantum Mechanics is incomplete, as well as Bell's work descendant therefrom. As a result, many inconsistencies and errors in contemporary discussions of nonlocality, as well as in Bell's Ansatz with respect to the laws of probabi…
We extend the validity of Hardy's nonlocality without inequalities proof to cover the case of special one-parameter classes of non-pure statistical operators. These mixed states are obtained by mixing the Hardy states with a completely chaotic noise or with a colored noise and they represent a realistic description of imperfect preparation processes of (pure) Hardy states in nonlocality experiments. Within such a framework we are able to exhibit a precise range of values of the parameter measuring the noise affecting the non-optimal preparation of an arbitrary Hardy state, for which it is stil…
Nonlocality is the most characteristic feature of quantum mechanics. John Bell, in his seminal 1964 work, proved that local-realism imposes a bound on the correlations among the measurement statistics of distant observers. Surpassing this bound rules out local-realistic description of microscopic phenomena, establishing the presence of nonlocal correlation. To manifest nonlocality, it requires, in the simplest scenario, two measurements performed randomly by each of two distant observers. In this work, we propose a novel framework where three measurements, two on Alice's side and one on Bob's …
We assess quantum non-locality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger (GHZ), W and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditio…
Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an Everettian or a statistical interpretation; and the conclusions r…
The concept of unified local field theory is considered. According to this concept the quantum description and the classical one must be the levels for investigation of some world solution of the unified field model. It is shown that in the framework of the unified local field theory there are nonlocal correlations between space separate events. Thus the experiments of Aspect type for testing of the Bell inequalities and for showing of the nonlocal correlations do not reject a possibility for description of matter with the unified local field theory. Advantages of such theory for new technolog…
There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L…
The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, any such experimental violation could always be explained in principle through models based on hidden influences propagating at a finite speed v>c, provided v is large enough. Here, we show that for any finite speed v with c<v<infinity, such models predict correlations that can be exploited for faster-than-light communication. This superluminal communication does not require access to any hidden …
Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state: \begin{align} \nonumber ρ_α= α\,|Φ^+ \rangle\langle Φ^+|+(1-α)\frac{\mathbb{1}}{4}. \end{align} We present two main results, consi…
The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other …
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 …
Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant "entangled" system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics coul…
The characterization of quantum correlations in terms of information-theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource. While bipartite entanglement and Bell inequality violation in this setting have been extensively studied, relatively little is known about their multipartite counterpart. In this paper, we apply and adapt the recently proposed definitions of multipartite nonlocality [Phys. Rev. A 88, 014102] to the three- and four-partite scenario to gain new insight on the resource aspect of multipartite nonlocal quantum correlation…
Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model - the LqHV (local quasi hidden variable) model [Loubenets, J. Math. Phys. 53, 022201 (2012)], incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows u…
Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that no…
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and besides its impact on our view of the world, it can be exploited for applications such as quantum cryptography and quantum computing. (...) Although entanglement and nonlocality are ordinarily regarded as one and the same, under close consideration this cannot be taken for granted. The reason for this is that entanglement is defined by the mathematical structure…
An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (non-universal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional non-stabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons cannot exhibit non-locality (in the sense of violating a Bell ineq…
The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality. In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, c…
The problem of computing the local hidden variable (LHV) value of a Bell inequality plays a central role in the study of quantum nonlocality. In particular, this problem is the first step towards characterizing the LHV polytope of a given scenario. In this work, we establish a relation between the LHV value of bipartite Bell inequalities and the mathematical notion of excess of a matrix. Inspired by the well developed theory of excess, we derive several results that directly impact the field of quantum nonlocality. We show infinite families of bipartite Bell inequalities for which the LHV valu…
Experimental attempts to implement quantum speedup of computations over the past 30 years have yielded a negative result, despite the absence of physical laws prohibiting such speedup. The article formulates the limitation of quantum formalism in the form of uncertainty "the complexity of the system - the accuracy of its description at the quantum level", and provides arguments in favor of its physical status. An experiment to determine this constant through Grover's algorithm is described. Rough estimates on the constant of this ratio are given, based on the possibility of applying the quantu…
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however,…
We show that the classical (mean-field) description of far from equilibrium superconductivity is exact in the thermodynamic limit for local observables but breaks down for global quantities, such as the entanglement entropy or Loschmidt echo. We do this by solving for and comparing exact quantum and exact classical long-time dynamics of a BCS superconductor with interaction strength inversely proportional to time and evaluating local observables explicitly. Mean field is exact for both normal and anomalous averages (superconducting order) in the thermodynamic limit. However, for anomalous expe…
Quantum computers promise dramatic advantages over their classical counterparts, but the answer to the most basic question "What is the source of the power in quantum computing?" has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via magic state distillation. This is a conceptually satisfying link because contextuality provides one of the fundamental characterizations of uniquely quantum phenomena and, moreover, magic state distillation is the leading model for experimentally realizing fault-toler…
Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schrödinger equation in the absence of hidden variables. This leads inevitably to a {\it many-minds interpretation}. The recent foundation of quasi-classical neural states in the brain (based on environmental decoherence) permits in principle a formal description of the whole chain of measurement interactions, including the {\it behavior} of conscious observers, without introducing any intermediate classical concepts (for macroscopic "pointer states") or "observables" (f…
Bell nonlocality is a cornerstone of quantum theory with applications in information processing ranging from cryptography to distributed computing and game theory. Indeed, it is known that Bell's theorem can be formally linked to Bayesian games, allowing the use of nonlocal correlations to advise players and thereby achieve new points of equilibrium that are unavailable classically. Here we generalize this link, proving the connection between multistage games of incomplete information with Bell scenarios involving the communication of measurement outcomes between the parties. We apply the gene…
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$π$i/k). This description is given with two objectives in mind. The first is to describe the algorithm in such a way as to make explicit the underlying and inherent control structure. The second is to make this algorithm accessible to a larger audience.
The dissipative properties of spatially nonlocal conductors are investigated in the context of quantum friction acting on an atom moving above a macroscopic body. The focus is on an extended version of the hydrodynamic model for the bulk material's electromagnetic response. It is shown that the standard hydrodynamic description is inadequate for evaluating the frictional force since it completely neglects Landau damping. The extended version of the model contains a frequency-dependent compressibility factor for the Fermi liquid and qualitatively resolves this issue. For a quantitative assessme…
