Showing papers on "Kochen–Specker theorem published in 2002"

Bell’s theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states

Abstract: A proof of Bell's theorem without inequalities valid for both inequivalent classes of three-qubit entangled states under local operations assisted by classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and $W,$ is described. This proof leads to a Bell inequality that allows more conclusive tests of Bell's theorem for three-qubit systems. Another Bell inequality involving both tri- and bipartite correlations is introduced which illustrates the different violations of local realism exhibited by the GHZ and $W$ states.

Bell’s Theorem: The Naive View of an Experimentalist

Abstract: It is a very emotional experience to contribute to this book commemorating of John Bell I first met John in 1975, a few months after reading his famous paper [1] I had been so strongly impressed by this paper, that I had immediately decided to do my “these d’etat” — which at that time, in France, could be a really long work — on this fascinating problem I definitely wanted to carry out an experiment “in which the settings are changed during the flight of the particles”, as suggested in the paper, and I had convinced a young professor at the Institut d’Optique, Christian Imbert, to support my project and to act as my thesis advisor He had advised me to go first to Geneva, to discuss my proposal with John Bell I got an appointment without delay, and I showed up in John’s office at CERN, quite nervous While I explained my planned experiment, he listened silently Eventually, I stopped talking, and the first question came: “Have you a permanent position?” After my positive answer, he started talking of physics, and he definitely encouraged me, making it clear that he would consider the implementation of variable analysers a fundamental improvement Remembering this first question reminds me both of his celebrated sense of humour and of the general atmosphere at that time about raising questions on the foundations of quantum mechanics Quite frequently there was open hostility, and in the best case, irony: “quantum mechanics has been vindicated by such a large amount of work by the smartest theorists and experimentalists; how can you hope to find anything with such a simple scheme, in optics, a science of the 19th century?” In addition to starting the experiment, I had then to develop a line of argument to try to convince the physicists I met (and among them some had to give their opinion about funding my project) After some not so successful attempts at quite sophisticated pleas, I eventually found out that it was much more efficient to explain the very simple and naive way in which I had understood Bell’s theorem And to my great surprise, that simple presentation was very convincing even with the most theoretically inclined interlocutors I was lucky enough to be able to present it in front of John Bell himself, and he apparently appreciated it I am therefore going to explain now how I understood Bell’s theorem twenty five years ago, and I hope to be able to communicate the shock I received, which was so strong that I spent eight years of my life working on this problem

A Kochen-Specker inequality

Abstract: By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low error rates, in the spirit of the Kochen-Specker theorem. Assuming that the errors are independent, an explicit error bound of 1.42% is derived, below which a Kochen-Specker contradiction occurs.

A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations

Abstract: We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4).

Exclusion of time in the theorem of Bell

Abstract: The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results these inequalities appear to prove that local hidden parameters cannot exist. This suggests to many that only instantaneous action at a distance can explain Einstein, Podolsky, Rosen (EPR) type of experiments. We show that Bell-type theories and proofs leading to the well-known inequalities completely exclude a large class of time dependencies in their considerations. Owing to the fact that the electrodynamics of moving bodies cannot be described by time-independent theories or models, we conclude that the Bell theorem cannot describe the physics of EPR experiments. We also show how hidden parameter theories that include time can obtain the quantum result.

Finite-precision measurement does not nullify the Kochen-Specker theorem

Abstract: It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. 83, 3751 (1999)], Kent [ibid. 83, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A 456, 2101 (2000)] leads to experimentally testable predictions that are in contradiction with those of quantum mechanics. Therefore, it is argued that the existence of dense Kochen-Specker-colorable sets must not be interpreted as a nullification of the physical impact of the Kochen-Specker theorem once the finite precision of real measurements is taken into account.

No time loophole in Bell's theorem: the Hess-Philipp model is nonlocal.

Abstract: Hess and Philipp recently claimed [(2001) Proc. Natl. Acad. Sci. USA 98, 14224-14227 and 14228-14233] that proofs of Bell's theorem have overlooked the possibility of time dependence in local hidden variables, hence the theorem has not been proven true. Moreover they present what is claimed to be a local realistic model of the EPR correlations. If this is true then Bell's theorem is not just unproven, but false. We refute both claims. First, we explain why time is not an issue in Bell's theorem, and second, we show that their hidden variables model violates Einstein separability. Hess and Philipp have overlooked the freedom of the experimenter to choose settings of a measurement apparatus at will: any setting could be in force during the same time period.

A simple demonstration of Bell's theorem involving two observers and no probabilities or inequalities

Abstract: This paper describes a device, consisting of a central source and two widely separated detectors with six switch settings each, that provides a simple gedanken demonstration of Bell's theorem without relying on either statistical effects or the occurrence of rare events. The mechanism underlying the operation of the device is revealed for readers with a knowledge of quantum mechanics.

Hidden Variables and Bell Inequalities on Quantum Logics

Abstract: In the quantum logic approach, Bell inequalities in the sense of Pitowski are related with quasi hidden variables in the sense of Deliyannis. Some properties of hidden variables on effect algebras are discussed.

Kochen-Specker theorem for finite precision spin-one measurements.

Abstract: Unsharp spin-one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way.

Bell’s Theorem, Information and Quantum Physics

Abstract: I had the great fortune to meet John Bell three times in my life. The first encounter was in 1975. I had been working since 1968 at the small Atom Institute in Vienna under Helmut Rauch on applying neutrons to investigate magnetic materials. Then he — together with Wolfgang Treimer and Ulrich Bonse [1] — developed the first crystal-based neutron interferometer as a tool to investigate the foundations of quantum mechanics. Because of my experience with polarized neutrons, I started to think about the role of the spin in such experiments and we were soon able to demonstrate the change of the sign of a spinor wave function upon a complete rotation by 2π [2]. So it was just in time that I discovered the announcement of an Erice workshop entitled “Thinkshops on Physics”, which was organized by John Bell together with Bernard d’Espagnat. The topic of this workshop was exactly experiments on the foundations of Quantum Physics. I went there and reported on our newest experimental results in neutron interferometry. I should mention that this was my first real encounter with the international scientific community. There, I heard for the first time about Bell’s theorem, about the Einstein-Podolsky-Rosen paradox, about entanglement, and the like. Needless to say that I did not get any real understanding what this was all about, but I got the hunch that something very important was being discussed. This meeting turned out to be very crucial in my life. There, I met a number of colleagues for the first time, some of whom later became personal friends. These include Mike Horne, Abner Shimony and also Val Telegdi. Mike Home and Val Telegdi then helped me to get to MIT and work with Cliff Shull at the neutron diffraction laboratory there. At that laboratory I also met Danny Greenberger later, and all this resulted in some of my most important collaborations. So it is fair to say that John Bell’s organization of that meeting was very important for me in many different ways.

Bell, Bohm, and Von Neumann: Some Philosophical Inequalities Concerning No-Go Theorems and the Axiomatic Method

Abstract: The present paper investigates the philosophical relationship between John von Neumann’s Nohidden-variable theorem and Bell’s inequalities. Bell erroneously takes the axiomatic method as implying a finality claim and thus ignores von Neumann’s strongly pragmatist stance towards mathematical physics. If one considers, however, Hilbert’s axiomatic method as a critical enterprise, Bell’s theorem improves von Neumann’s by defining a more appropriate notion of ‘ hidden variable’ that permits one to include Bohm’s interpretation which recovers the predictive content of quantum mechanics. Contrary to Bell’s belief, accepting this model does not require adopting the metaphysically realist Bohm picture. If one takes the latter as a physical research programme one sees that it only partly disputes a common domain of facts with the mathematically oriented research programme of von Neumann.

The Kochen-Specker Theorem for Finite Precision Spin 1-Measurements

Abstract: Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.

Bell's theorem in the presence of classical communication

Abstract: I explain what kinds of correlation or even direct classical communication between detectors invalidate Bell's theorem, and what kinds do not.

A Kochen-Specker Theorem for Unsharp Spin 1 Observables

Abstract: Unsharp spin observables are shown to arise from the fact that a residual uncertainty about the actual alignment of the measurement device remains. If the uncertainty is below a certain level, and if the distribution misalignments is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.

Bell's theorem and chemical potential

Abstract: Chemical potential is a property which involves the effect of interaction between the components of a system, and it results from the whole system. In this paper, we argue that for two particles which have interacted via their spins and are now spatially separated, the so-called Bell's locality condition implies that the chemical potential of each particle is an individual property. Here is a point where quantum statistical mechanics and the local hidden variable theories are in conflict. Based on two distinct concepts of chemical potential, the two theories predict two different patterns for the energy levels of a system of two entangled particles. In this manner, we show how one can distinguish the non-separable features of a two-particle system.

Exclusion of correlation in the theorem of Bell

Abstract: Several fatal defects in recent defenses of Bell's theorem are identified It is shown again that ``proofs'' of the existence of non-locality are not valid because they inadvertently exclude all correlation A fully classical simulation of EPR correlations, based on using Malus' Law for both photocurrent generation and for the ``coincidence circuitry,'' is described

Logical Inconsistencies in Proofs of the Theorem of Bell

Abstract: We discuss a class of proofs of Bell-type inequalities that are based on tables of potential outcomes These proofs state in essence: if one can only imagine (or write down in a table) the potential outcome of a hidden parameter model for EPR experiments then a contradiction to experiment and quantum mechanics follows We show that these proofs do not contain hidden variables that relate to time or, if they do, lead to logical contradictions that render them invalid

Classical information and Mermin's non-technical proof of the theorem of Bell

Abstract: We show that Mermin's reasoning against our refutation of his non-technical proof for Bell-type inequalities is of limited significance or contains mathematical inconsistencies that, when taken into account, do not permit his proof to go forward. Our refutation therefore stands.

Comment on "How the No-Cloning Theorem Got its Name"

Abstract: A review by A. Peres [quant-ph/0205076] appears recently. It is difficult to add something to such kind of fundamental themes, but here is briefly presented some ideas about challenges of the no-cloning theorem and imaginary modifications of quantum mechanics, that could make precise cloning possible.

Comment on Mermin's Recent Proof of the Theorem of Bell

Abstract: Mermin states in a recent paper that his nontechnical version of Bell's theorem stands and is not invalidated by time and setting dependent instrument parameters as claimed in one of our previous papers. We identify a number of misinterpretations (of our definitions) and mathematical inconsistencies in Mermin's paper and show that Mermin's conclusions are therefore not valid: his proof does not go forward if certain possible time dependencies are taken into account.

MGP versus Kochen-Specker condition in hidden variables theories

Abstract: Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an operational viewpoint, which suggests that a weaker condition (MGP) should be adopted in place of it. This leads one to introduce a class of hidden parameters theories in which contextuality can, in principle, be avoided, since the proofs of the Bell-Kochen-Specker theorem break down. A simple model recently provided by the author for an objective interpretation of quantum mechanics can be looked at as a noncontextual hidden parameters theory, which shows that such theories actually exist.

Transcendental Structuralism in Physics: An alternative to Structural Realism

Abstract: In physics, structures are good candidates for the role of transparadigmatic invariants, which entities can no longer play. This is why structural realism looks more credible than standard entity realism. But why should structures be stable, rather than entities ? Here, structural realists have no answer ; they content themselves with the mere observation that this is how things stand. By contrast, transcendental structuralism (a byproduct of Kant’s transcendental idealism) can easily make sense of this fact. Indeed, it shows that when knowledge bears on phenomena, namely on the emergent byproduct of a relation between the explorer and what is to be explored, this knowledge necessarily bears on relations between such phenomena. After a development on the clarifying power of transcendental structuralism, I turn to an early transcendental structuralist interpretation of quantum mechanics proposed by Jean-Louis Destouches (1909-1980). Destouches, an early French philosopher of physics, was a student of Louis de Broglie. He recasted in the 1940 the very concept of physical theory in the light of quantum physics. According to him, whenever phenomena are inextricably relative to the experimental set-up, a physical theory cannot provide anything beyond a list of interconnected predictions for future facts given a relevant class of past facts. In his general mathematical theory of predictions, the Ψ-functions of quantum mechanics do not refer to some “real” waves; they are shown to be nothing but the formal expression of the phenomena’s being relative to incompatible experimental contexts. Since the quantization of variables can itself be derived from a wave-mechanical formalism, it becomes clear that the most prominent features of quantum mechanics are a mere consequence of contextuality. Destouches thus proved that it is easy to make sense of quantum mechanics provided a reflective attitude is adopted. By contrast, too many difficulties arise when one tries at any cost to make quantum mechanics intelligible within a purely ontological framework.