It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally -- notwithstanding Bell's theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit's local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.
We investigate non-locality distillation using measures of non-locality based on the Elitzur-Popescu-Rohrlich decomposition. For a certain number of copies of a given non-local correlation, we define two quantities of interest: (i) the non-local cost, and (ii) the distillable non-locality. We find that there exist correlations whose distillable non-locality is strictly smaller than their non-local cost. Thus non-locality displays a form of irreversibility which we term bound non-locality. Finally we show that non-local distillability can be activated.
Quantum non-locality based on the well-known Bell inequality is of kinematic nature. A different type of quantum non-locality, the non-locality of the quantum equation of motion, is recently put forward with connection to the Aharonov-Bohm effect [Nature Phys. 6, 151 (2010)]. Evolution of the displacement operator provides an example to manifest such dynamic quantum non-locality. We propose an experiment using single-atom interferometry to test such dynamic quantum non-locality. We show how to measure evolution of the displacement operator with clod atoms in a spin-dependent optical lattice po…
In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject, we consider if quantum non-locality, and the friction it carries with special relativity, can eventually find a "solution" by considering higher dimensional spaces.
We prove that by adopting a strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, the proofs of the known non-locality theorems fail in showing that quantum mechanics violates the principle of locality and reality.
A new interpretation of nonrelativistic quantum mechanics explains the violation of Bell's inequality by maintaining realism and the principle of locality.
We discuss the locality problem in relativistic and nonrelativistic quantum theory. We show that there exists a formulation of quantum theory that, on one hand, preserves the mathematical apparatus of the standard quantum mechanics and, on the other hand, ensures the satisfaction of the locality condition for each individual event including the measurement procedure. As an example, we consider the scattering from two slits.
A critique to the article by C.A. Fuchs, N.D. Mermin, and R.Schack, "An introduction to QBism with and application to the locality of quantum mechanics" that appeared in Am. J. Phys. 82 (8), 749-754 (2014)
The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables that depend on gauge fields and gravity as well as the wave function are used in order to try to understand and minimize this conflict within the frame-work of these two theories. Applications are made to the Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and gravity.
We investigate the situation in which no information can be transferred from a quantum system B to a quantum system A, even though both interact with a common system C.
Quantum non-locality is normally defined via violations of Bell's inequalities that exclude certain classical hidden variable theories from explaining quantum correlations. Another definition of non-locality refers to the wave-function collapse thereby one can prepare a quantum state from arbitrary far away. In both cases one can debate on whether non-locality is a real physical phenomenon, e.g. one can employ formulations of quantum mechanics that does not use collapse, or one can simply refrain from explaining quantum correlations via classical hidden variables. Here we point out that there …
Many of the contemporary formulations of quantum mechanics describe the marginal probability distributions of entangled many-body systems in a non-local way. Unlike the non-locality of joint distributions, the non-locality of marginal distributions is not forced by theory or experiment. This paper investigates the issue in the context of the Copenhagen, de Broglie-Bohm and sum-over-paths interpretations. A dissociation between information flow into quantum subsystems and the tensor product structure of wavefunctions is highlighted in connection to the problem.
Is information causality a new physical principle? To answer this question, we first analytically derive the criteria of emergence of quantum correlations from information causality. Then it is shown that, as emergence criteria of quantum correlations, information causality and uselessness of coupler-based non-locality swapping can be regarded equivalent. Therefore, incapability of non-locality swapping using a coupler is as powerful as information causality in the single-out of quantum physics from generalized non-signalling models.
In this paper we show that quantum non-locality can be super-activated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. Moreover, previous results suggest that such Bell violations can be very large.
A view of emission and absorption of photons by atoms, which was proposed by Max Planck, is recalled. A direct experiment that could corroborate or refute that view is defined.
We give an example of fulfillment of the condition of locality--no information transfer between certain subsystems--in a tripartite quantum system whose dynamics can not be decomposed (non-sequential dynamics of the system). The three subsystems ($A$, $B$ and $C$) are designed such that $C$ interacts simultaneously with both $A$ and $B$, while there is not any interaction between $A$ and $B$. On this basis, we emphasize validity of the condition of locality in a realistic physical situation.
We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell inequalities and quantum Bell inequalities in bipartite scenarios with dichotomic observables. We discuss how to improve the latter approximation and how to extend our ideas to scenarios with more than two outcomes per setting.
The locality problem of quantum measurements is considered in the framework of the algebraic approach. It is shown that contrary to the currently widespread opinion one can reconcile the mathematical formalism of the quantum theory with the assumption of the existence of a local physical reality determining the results of local measurements. The key quantum experiments: double-slit experiment on electron scattering, Wheeler's delayed-choice experiment, the Einstein-Podolsky-Rosen paradox, and quantum teleportation are discussed from the locality-problem point of view. A clear physical interpre…
A correlation measure relating to measured and unmeasured local quantities in quantum mechanics is introduced, and is then applied to assess the locality implications for Bell/CHSH and similar set-ups. This leads to some interesting results, and the scheme is extended to the generalized no-signalling boxes framework. Some questions are raised about the use of counterfactual reasoning in quantum mechanics.
By constructing the quantum state in high-dimensional probability tensor, we find the quantum magic square(QMS) may stand as an ideal means of characterizing the non-local phenomena, i.e. the separability, entanglement, two/one-way steering, and Bell non-locality, etc. In this scheme, different types of non-locality exhibit distinctive inner structures of the probability tensor, which are observable in form of the partial sum of the tensor components. In application, we prove the Bell and GHZ theorems, and demonstrate that the uncertainty relation may rate the non-locality, from Bell locality …
Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there i…
Non-locality consists in the existence of non-classical correlations between local measurements. So far, it has been investigated mostly in isolated quantum systems. Here we show that non-local correlations are present, can be detected and might be robust against noise also in many-body open quantum systems, both in the steady-state and in the transient regime. We further discuss the robustness of non-local correlations when the open quantum system undergoes repeated measurements, a relevant scenario for quantum cryptography.
In a previous paper [arXiv:quant-ph/9906007] Hayden and I proved, using the Heisenberg picture, that quantum physics satisfies Einstein's criterion of locality. Wallace and Timpson have argued that certain transformations of the Heisenberg- picture description of a quantum system must be regarded as leaving invariant the factual situation being described, and that taking this into account reveals that Einstein's criterion is violated after all. Here I vindicate the proof and explain some misconceptions that have led to this and other criticisms of it.
Studying generalized non-local theories brings insight to the foundations of quantum mechanics. Here we focus on non-locality swapping, the analogue of quantum entanglement swapping. In order to implement such a protocol, one needs a coupler that performs the equivalent of quantum joint measurements on generalized `box-like' states. Establishing a connection to Bell inequalities, we define consistent couplers for theories containing an arbitrary amount of non-locality, which leads us to introduce the concepts of perfect and minimal couplers. Remarkably, Tsirelson's bound for quantum non-locali…
Non-locality and steering are both non-classical phenomena witnessed in Nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, "post-quantum steering" has been described, which is steering that cannot be reproduced by measurements on entangled states, but do not lead to superluminal signalling. In this work we present a framework based on the s…
We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non-LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreas…
The emergence of the generalized uncertainty principle and the existence of a non-zero minimal length are intertwined. On the other hand, the Heisenberg uncertainty principle forms the core of the EPR paradox. Subsequently, here, the implications of resorting to the generalized uncertainty principle (or equally, the minimal length) instead of the Heisenberg uncertainty principle on the quantum non-locality are investigated through focusing on the Franson experiment in which the uncertainty relation is the backbone of understanding and explaining the results.
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the s…
It is shown that, in order to avoid unacceptable nonlocal effects, the free parameters of the general Doebner-Goldin equation have to be chosen such that this nonlinear Schrödinger equation becomes Galilean covariant.
The structure of Bell-type inequalities detecting genuine multipartite non-locality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite non-locality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally we discuss the thightness and quantum me…
By studying generalized non-signalling theories, the hope is to find out what makes quantum mechanics so special. In the present paper, we revisit the paradigmatic model of non-signalling boxes and introduce the concept of a genuine box. This will allow us to present the first generalized non-signalling model featuring quantum-like dynamics. In particular, we present the coupler, a device enabling non-locality swapping, the analogue of quantum entanglement swapping, as well as teleportation. Remarkably, part of the boundary between quantum and post-quantum correlations emerges in our study.
Subsystems of entangled quantum systems are not traditionally described in a local way. This paper begins to address the issue by constructing an explicit local hidden variable theory for quantum subsystems. The interpretation is based on a modified sum-over-paths approach, where the paths of the subsystem obtain information about the external system during interactions. The interpretation utilizes the conception that there is a dissociation between the tensor product structure of wavefunctions and information flow into quantum subsystems.
Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition in…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former system as a subsystem. Hence, the bigger system acts as a reference system. It is shown that quantum mechanics can be reformulated in accordance with this new physical assumption. There is an important consequence of this dependence: states may not be comparable, i.e., they cannot be checked by suitable measurements simultaneously. This special circumstance i…
It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply classical concepts and introduce probabilities in a manner inconsistent with the Hilbert space structure of standard quantum mechanics. Instead, Einstein locality is a valid quantum principle: objective properties of individual quantum systems do not change when something is done to another noninteracting system. There is no reason to suspect any conflict bet…
Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of `gauge freedom' according to which mathematically distinct states are physically equivalent. Once this gauge freedom is taken into account, their formulation is no longer local.
Research Institute for Astronomy and Astrophysics of Maragha（马拉盖天文与天体物理研究所）；Izmir Institute of Technology（伊兹密尔理工大学）；Khazar University（哈扎尔大学）；Dogus University（多乌斯大学）
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this representation as a reference-and-imbedding-structure, the foundations of an intelligible reconstruction of the Hilbert-Dirac formulation of Quantum Mechanics is developed. Inside this reconstruction the measurement problem as well as the other major problems raised by the quantum mechanical formalism, dissolve.
In order to study N-locality without inputs in long lines and in configurations with loops, e.g. the triangle, we introduce a natural joint measurement on two qubits different from the usual Bell state measurement. The resulting quantum probability $p(a_1,a_2,...,a_N)$ has interesting features. In particular the probability that all results are equal is that large, while respecting full symmetry, that it seems highly implausible that one could reproduce it with any N-local model, though - unfortunately - I have not been unable to prove it.
According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the interaction between the measured system and measuring apparatus using Born's statistical interpretation. But it is conceivable that detailed analysis of all possible Bell experiments would allow the compatibility of quantum theory and local realism. The difficulties of theory and experiment are closely related.
The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of modular momentum associated with such phenomena cannot be directly observed, it has been suggested that effects induced by this exchange can be measured experimentally using weak measurements of pre- and post-selected ensembles of particles. This paper reports on such an optical experiment that yielded measured weak values that were consistent with the theore…
It is often supposed that a quantum system is not disturbed without state change. In a recent debate, this assumption is used to claim that the operator-based disturbance measure, a broadly used disturbance measure, has an unphysical property. Here, we show that a quantum system possibly incurs an operationally detectable disturbance without state change to rebut the claim. Moreover, we establish the reliability, formulated as soundness and locality, of the operator-based disturbance measure, which, we show, quantifies the disturbance on an observable that manifests in the time-like correlatio…
Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of quantum mechanically incompatible quantities. We first recall several contradictions arising between the assumption of a joint distribution for incompatible observables and the probability structure of quantum-mechanics, and conclude that Bell's theorem is not expected to be relevant to quantum phenomena described by non-commuting observables, irrespective …
Stapp's counterfactual argument for quantum nonlocality based upon a Hardy entangled state is shown to be flawed. While he has correctly analyzed a particular framework using the method of consistent histories, there are alternative frameworks which do not support his argument. The framework dependence of quantum counterfactual arguments, with analogs in classical counterfactuals, vitiates the claim that nonlocal (superluminal) influences exist in the quantum world. Instead it shows that counterfactual arguments are of limited use for analyzing these questions.
We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum-classical boundary. The latter include photon added thermal and photon added coherent sources, experimentally investigated recently by Zavatta et al. [Phys. Rev. Lett. 103, 140406 (2009)]. The key quantity in our investigations is the visibility of the corresponding photon-photon correlation function. We present explicit results on the violations of the Cauchy-Schwarz inequality - which is a measure of nonclassicality - as well as of …
We present a simple model demonstrating that time-symmetric relativistic interactions can account for correlations violating the Bell inequalities while avoiding conspiracies as well as the commitment to instantaneous influences. Based on an explicit statistical analysis of this model, we emphasize the essential virtues and problems of such an account and discuss its relation to Bell's theorem.
We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism whereby it is the entanglement of the modes that can be populated by the particles what really matters and not the particles themselves. Indeed, by means of a metr…
Recently, a series of different measures quantifying memory effects in the quantum dynamics of open systems has been proposed. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment which substantially simplifies its numerical and experimental determination, and fully reveals the locality and universality of non-Markovianity in the quantum state space. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degre…
Quantum cognition is an emerging field making uses of quantum theory to model cognitive phenomena which cannot be explained by classical theories. Usually, in cognitive tests, subjects are asked to give a response to a question, but in this paper, we just observed the subjects' behaviour and the question and answer method was not applied in order to prevent any mental background on participants' minds. Finally, we examined the experimental data on Hardy's non-locality argument (HNA), and we noticed the violation of HNA in human behaviour.
