The reason for recalling this old paper is the ongoing discussion on the attempts of circumventing certain assumptions leading to the Bell theorem (Hess-Philipp, Accardi). If I correctly understand the intentions of these Authors, the idea is to make use of the following logical loophole inherent in the proof of the Bell theorem: Probabilities of counterfactual events A and A' do not have to coincide with actually measured probabilities if measurements of A and A' disturb each other, or for any other fundamental reason cannot be performed simulaneously. It is generally believed that in the context of classical probability theory (i.e. realistic hidden variables) probabilities of counterfactual events can be identified with those of actually measured events. In the paper I give an explicit counterexample to this belief. The "first variation" on the Aerts model shows that counterfactual and actual problems formulated for the same classical system may be unrelated. In the model the first probability does not violate any classical inequality whereas the second does. Pecularity of the Bell inequality is that on the basis of an in principle unobservable probability one derives probabilities of jointly measurable random variables, the fact additionally obscuring the logical meaning of the construction. The existence of the loophole does not change the fact that I was not able to construct a local model violating the inequality with all the other loopholes eliminated.
So far, all experimental tests of Bell inequalities which must be satisfied by all local realistic hidden-variable theories and are violated by quantum mechanical predictions have left at least one loophole open. We propose a feasible setup allowing for a loophole-free test of the Bell inequalities. Two electron spin qubits of phosphorus donors in semiconductors in different cavities 300 m apart are entangled through a bright coherent light and postselections using homodyne measurements. The electron spins are then read out randomly and independently by Alice and Bob, respectively, with unity …
We present a scheme to demonstrate loophole-free Bell inequality violation where the entanglement between photon pairs is transferred to solid state (spin) qubits mediated by cavity QED interactions. As this transfer can be achieved in a heralded way, our scheme is basically insensitive to losses on the channel. This makes it appealing for the implementation of quantum information protocols based on nonlocality, such as device-independent quantum key distribution. We consider potential experimental realisations of our scheme using single atom, colour centre and quantum dot cavity systems.
A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of particles have free will. The construction uses random variables which are not jointly measurable in a single run of an experiment and the hidden variables have a nonsymmetric probability density. Such random variables are complementary but still fully classical. An assumption that classical random variables cannot satisfy any form of complementarity principle is f…
We exhibit a classical model free from any paradox which exactly simulates the spin EPR test. We conclude that Bell's inequality violation is a strictly classical phenomenon, contrary to a general belief.
One of the most striking non-classical features of quantum mechanics is in the correlations it predicts between spatially separated measurements. In local hidden variable theories, correlations are constrained by Bell inequalities, but quantum correlations violate these. However, experimental imperfections lead to "loopholes" whereby LHV correlations are no longer constrained by Bell inequalities, and violations can be described by LHV theories. For example, loopholes can emerge through selective detection of events. In this letter, we introduce a clean, operational picture of multi-party Bell…
A classical model is presented for the features of parametric down-conversion and homodyne detection relevant to recent proposed ``loophole-free'' Bell tests. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If cit is not, then the experiments will fail in their initial concept, since both quantum theorists and local r…
In a recent article Hensen et al. [Nature 526, 682 (2015)] report on a sophisticated Bell experiment, simultaneously closing, for the first time, loopholes for local hidden-variable theories (HVTs). The authors claim that 'local realism' has been refuted, under certain natural assumptions. The aim of the present Comment is twofold. First, it is urged that the class of local HVTs that is eliminated by the reported experiment should be specified in greater detail than is done by the authors. Second, it is argued that the class of local HVTs that still survives is wide and natural. For instance, …
Recent proposed ``loophole-free'' Bell tests are discussed in the light of classical models for the relevant features of optical parametric amplification and homodyne detection. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If it is not, then the experiments will fail in their initial concept, since both quantum the…
Semi-device-independent quantum protocols realize information tasks - e.g. secure key distribution, random access coding, and randomness generation - in a scenario where no assumption on the internal working of the devices used in the protocol is made, except their dimension. These protocols offer two main advantages: first, their implementation is often less demanding than fully-device-independent protocols. Second, they are more secure than their device-dependent counterparts. Their classical analogous is represented by random access codes, which provide a general framework for describing on…
We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this proof gives eta > 0.69. This efficiency is lower than that required for previous proposals.
The inequalities proposed in [Phys. Rev. Lett. 105, 170404 (2010)] are not Bell's inequalities in the usual sense: there are local classical models that violate these inequalities. Thus, their violation demonstrates nonlocality only under assumptions about the physical implementation and moreover they cannot be used as a device-independent test of nonlocality.
We demonstrate that different kind of mesoscopic quantum states of light can be efficiently generated from a simple iterative scheme using homodyne heralding. These states exhibit strong non-classical features, and are of great interest for many applications such as quantum error-correcting codes or fundamental testings. On this basis we propose a protocol allowing a large loophole-free violation of a CHSH-type Bell inequality with a remarkable robustness to line losses.
The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682-686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of $2.35 \pm 0.18$, in agreement with the first run, yielding an overall value of $S = 2.38 \pm 0.14$. We calculate the resulting $P$-values of the second experiment and of the combined Bell tests. We provide an addition…
A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory itself is both local and realistic when properly interpreted using a quantum Hilbert space rather than the classical hidden variables used to derive Bell inequalities. There is no spooky action at a distance in the real world we live in if it is governed by the laws of quantum mechanics.
The coincidence-time loophole was identified by Larsson & Gill (Europhys. Lett. 67, 707 (2004)); a concrete model that exploits this loophole has recently been described by De Raedt et al. (Found. Phys., to appear). It is emphasized here that De Raedt et al.'s model is experimentally testable. De Raedt et al.'s model also introduces contextuality in a novel and classically more natural way than the use of contextual particle properties, by introducing a probabilistic model of a limited set of degrees of freedom of the measurement apparatus, so that it can also be seen as a random field model. …
A local hidden variable model exploiting the detection loophole to reproduce exactly the quantum correlation of the singlet state is presented. The model is shown to be compatible with both the CHSH and the CH Bell inequalities. Moreover, it bears the same rotational symmetry as spins. The reason why the model can reproduce the quantum correlation without violating the Bell theorem is that in the model the efficiency of the detectors depends on the local hidden variable. On average the detector efficiency is limited to 75%.
For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, num…
We apply a distance-based Bell-test analysis method [E. Knill et al., Phys. Rev. A. 91, 032105 (2015)] to three experimental data sets where conventional analyses failed or required additional assumptions. The first is produced from a new classical source exploiting a "coincidence-time loophole" for which standard analysis falsely shows a Bell violation. The second is from a source previously shown to violate a Bell inequality; the distance-based analysis agrees with the previous results but with fewer assumptions. The third data set does not show a violation with standard analysis despite the…
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by $398\,\mathrm{m}$ with fast an…
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is …
Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole and the locality loophole simultaneously is highly desirable and remains challenging. A novel approach to a loophole-free Bell tests is based on amplification of the entangled photons, i.e.\@ on macroscopic entanglement, which optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by the classical detectors. An…
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define and, if not sufficiently accurate, they provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully sepa…
We develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can stop performing trials early, as soon as the desired amount of randomness is extractable. It can be used with arbitrary, partially known and time-dependent probabilities for the random settings choices. Furthermore, it is suitable for application to experimental configurations with low Bell violation per trial, such as current optical loophole-free Bell tes…
Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of …
According to recent reports, the last loopholes in testing Bell's inequality are closed. It is argued that the really important task in this field has not been tackled yet and that the leading experiments claiming to close locality and detection efficiency loopholes, although making a very significant progress, have conceptual drawbacks. The important task is constructing quantum devices which will allow winning games of certain correlated replies against any classical team. A novel game of this type is proposed.
Quantum correlations are critical to our understanding of nature, with far-reaching technological and fundamental impact. These often manifest as violations of Bell's inequalities, bounds derived from the assumptions of locality and realism, concepts integral to classical physics. Many tests of Bell's inequalities have studied pairs of correlated particles; however, the immense interest in multi-particle quantum correlations is driving the experimental frontier to test systems beyond just pairs. All experimental violations of Bell's inequalities to date require supplementary assumptions, openi…
This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern-Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions re retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both loc…
Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. However, an explicit counterexample shows that a new class of local realistic models, based on generalized arithmetic and calculus, can exactly reconstruct rotationally symmetric quantum probabilities typical of two-electron singlet states. Observable probabilities are consistent with the usual arithmetic employed by macroscopic observers, but counterfactual aspects of Bell's theorem are sensitive to the choice of hidden-variable arithmetic and calculus. The model is classical in the sense of Einste…
Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental test for the physics laws of nature, and on the other hand, it can be also applied in varieties of device independent tasks such as quantum key distribution and random number generation. In practice, loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions. In this work, we focus on the randomness (freewill) loophole and investigate the randomness requirement in a well-known Bell test, the Clauser-Horne test, under various condit…
Quantum non-locality has been experimentally investigated by testing different forms of Bell's inequality, yet a loophole-free realization has not been achieved up to now. Much less explored are temporal Bell inequalities, which are not subject to the locality assumption, but impose a constrain on the system's time-correlations. In this paper, we report on the experimental violation of a temporal Bell's inequality using a nitrogen vacancy defect (NV) in diamond and provide a novel quantitative test of quantum coherence. We therefore present a new technique to initialize the electronic state of…
A recent claim by Meyer, Kent and Clifton (MKC), that their models ``nullify'' the Kochen-Specker theorem, has attracted much comment. In this paper we present a new counter-argument, based on the fact that a classical measurement reveals, not simply a pre-existing value, but pre-existing classical information. In the MKC models measurements do not generally reveal pre-existing classical information. Consequently, the Kochen-Specker theorem is not nullified. We go on to prove a generalized version of the Kochen-Specker theorem, applying to non-ideal quantum measurements. The theorem was inspir…
From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a num…
I discuss three issues connected to Bell's theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars Under Local Realism), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell's list of four positions to hold in the light of his results. Levy's (1935) theory of martingales, and Fisher's (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell's conclusions are inde…
The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It is measured with a Stern-Gerlach array whose outputs are divided into two classes, spin-up and spin-down, in correspondence to the two spots observed on a detection screen. The spot's finite size is attributed to imperfections of the measuring device. This assumption turns the experimental output into a dichotomic, discrete one, thereby allowing the assignme…
An experimentally observed violation of Bell's inequality is supposed to show the failure of local realism to deal with quantum reality. However, finite statistics and the time sequential nature of real experiments still allow a loophole for local realism, known as the memory loophole. We show that the randomized design of the Aspect experiment closes this loophole. Our main tool is van de Geer's (2000) supermartingale version of the classical Bernstein (1924) inequality guaranteeing, at the root n scale, a not-heavier-than-Gaussian tail of the distribution of a sum of bounded supermartingale …
A common experimental strategy for demonstrating non-classical correlations is to show violation of a Bell inequality by measuring a continuously emitted stream of entangled photon pairs. The measurements involve the detection of photons by two spatially separated parties. The detection times are recorded and compared to quantify the violation. The violation critically depends on determining which detections are coincident. Because the recorded detection times have "jitter", coincidences cannot be inferred perfectly. In the presence of settings-dependent timing errors, this can allow a local-r…
In this thesis, we study about three subjects 1- Classical simulation of two spin-$s$ singlet correlations for all $s$ involving spin measurements, 2- Quantum correlations in successive single spin measurements, 3- Non locality without inequality for almost all two-qubit entangled states based on Cabello's non locality argument.
With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is consumed. Here, we devise a device-independent spot-checking protocol that consumes only uniform bits without req…
Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system.
The class of two-interacting-impurity spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be exactly mapped into two independent standard single-impurity spin-boson models where the role of the tunnelling parameter is played by the spin-spin coupling. The dynamics of the magnetization is analysed for different levels of (an)isotropy. Further, the existence of a decoherence-free subspace as well as of both classical and quantum (first-order and Kosterlitz-Thouless type) phase transitions, in the Omhic regime, is brought to light.
We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states form a convex set C, which we fully characterize for a spin-1/2 and a spin-1. For arbitrary spin, we provide ``non-classicality witnesses''. For bipartite systems, C forms a subset of all separable states. A state of two spins-1/2 belongs to C if and only if it is separable, whereas for a spin-1/2 coupled to a spin-1, there are separable states which do not…
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
We show there exists an exact and continuous gauge transformation between the Hamilton-Jacobi equation of classical mechanics, and the time-dependent Schrodinger equation of quantum mechanics. The transformation parameter is spin-dependent, and is a function of the quantum potential of Bohmian mechanics.
In this continuation paper the Schrödinger equation for the half-integral spin eigenfunctions is obtained and solved. We show that all the properties already derived using the Heisemberg matrix calculation and Pauli's matrices are also obtained in the realm of these analytical functions. We also show that Einstein-Bose condensation for fermions is expected. We then conclude this series of two papers on the concept of classical spin.
A nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a classically driven nonlinear differential equation with dissipation and a semi-classical interpretation of the torque on a spin magnetic moment in the presence of a realistic magnetic field, which will represent two equilibrium positions. The highly complicated driven nonlinear dissipative semi-classical model is used to introduce chaos, which is necessary to produce the correct statistical quantum results. The resemblance between this semi-classical spin model an…
We introduce the concept of "absolutely classical" spin states, in analogy to absolutely separable states of bi-partite quantum systems. Absolutely classical states are states that remain classical under any unitary transformation applied to them. We investigate the maximum ball of absolutely classical states centered on the fully mixed state that can be inscribed into the set of classical states, and derive a lower bound for its radius as function of the total spin quantum number. The result is compared to the case of absolutely separable states.
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a simmetry property related to the Lie algebra to which it is associated. The classical approach will be paraleled with the usual quantum one to stress their formal similarities and epistemological differences. The important problem of Einstein-Bose condensation for fermions will also be addressed.
We give a classical protocol to exactly simulate quantum correlations implied by a spin-$s$ singlet state for the infinite sequence of spins satisfying $(2s + 1) = 2^{n}$, in the worst-case scenario, where $n$ is a positive integer. The class of measurements we consider here are only those corresponding to spin observables. The required amount of communication is found to be $log_{2}d$ where $d = 2s + 1$ is the dimension of the spin-$s$ Hilbert space.
The generation of non-classical states of large quantum systems has attracted much interest from a foundational perspective, but also because of the significant potential of such states in emerging quantum technologies. In this paper we consider the possibility of generating non-classical states of a system of spins by interaction with an ancillary system, starting from an easily prepared initial state . We extend previous results for an ancillary system comprising a single spin to bigger ancillary systems and the interaction strength is enhanced by a factor of the number of ancillary spins. D…
Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to the quantum/classical interface is based on a formulation of relativistic classical mechanics that uses spinors. Spinors and projectors arise naturally in the Clifford's geometric algebra of physical space and not only provide powerful tools for solving problems in classical electrodynamics, but also reproduce a number of quantum results. In particular, many …
We address the propagation of the spin along classical trajectories for a 1/2-spin particle obeying the Dirac equation with scalar potentials. Focusing on classical trajectories as the exact propagation of wave-function discontinuities we find an explicit spin-transport law for the case of the Dirac oscillator. In the general case we examine the spin propagation along classical trajectories emerging as an approximation of the quantum dynamics via the mechanical analog of the optical eikonal asymptotic approach. Throughout we establish as many parallels as possible with the equivalent situation…
The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. For the generalised $θ$-angled spin-boson model, we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, for the quantum spin-boson model we prove, by carefully taking a large spin limit, that Bohr's quantum-classical correspondence persists at all coupling strengths. This correspondence gives insight into the conditions for a coupled quantum spin to be well-approximated…
