In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then \"we are forced to give up the view that there is one single reality.\" Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent \"single-world\" interpretation of the theory.

}, url = {https://arxiv.org/abs/1804.03267}, author = {Jeffrey Bub} } @book {2249, title = {Totally random: why nobody understands quantum mechanics (a serious comic on entanglement)}, year = {2018}, publisher = {Princeton University Press}, organization = {Princeton University Press}, author = {Jeffrey Bub and Tanya Bub} } @article {2097, title = {Why Bohr was (Mostly) Right}, year = {2017}, month = {2017/11/05}, abstract = {After a discussion of the Frauchiger-Renner argument that no \“singleworld\” interpretation of quantum mechanics can be self-consistent, I propose a \“Bohrian\” alternative to many-worlds or QBism as the rational option.

}, url = {https://arxiv.org/abs/1711.01604}, author = {Jeffrey Bub} } @book {1318, title = {Bananaworld: Quantum Mechanics for Primates}, year = {2016}, month = {2012/11/13}, publisher = {Oxford University Press}, organization = {Oxford University Press}, abstract = {This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The \&$\#$39;no go\&$\#$39; theorems tell us that we can\&$\#$39;t shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

}, url = {http://arxiv.org/abs/1211.3062v2}, author = {Jeffrey Bub} } @article {1602, title = {Whose Information? Information About What?}, journal = {Quantum [Un]Speakables II: 50 Years of Bell{\textquoteright}s Theorem}, year = {2016}, month = {2016/01/01}, author = {Jeffrey Bub and Anton Zeilinger and Reinhold Bertlmann} } @article {1599, title = {The Measurement Problem from the Perspective of an Information Theoretic Interpretation of Quantum Mechanics}, journal = {Entropy}, volume = {17}, year = {2015}, month = {10/28/2015}, pages = {7374-7386}, abstract = {The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems.}, doi = {10.3390/e17117374}, url = {http://www.mdpi.com/1099-4300/17/11/7374}, author = {Jeffrey Bub} } @article {1601, title = {Quantum Entanglement and Information}, journal = {The Stanford Encyclopedia of Philosophy}, year = {2015}, month = {02/07/2015}, abstract = {Quantum entanglement is a physical resource, like energy, associated with the peculiar nonclassical correlations that are possible between separated quantum systems. Entanglement can be measured, transformed, and purified. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems. The general study of the information-processing capabilities of quantum systems is the subject of quantum information theory.}, url = {http://plato.stanford.edu/archives/sum2015/entries/qt-entangle/}, author = {Jeffrey Bub and Edward N. Zalta} } @article {1600, title = {"Einstein and Bohr Meet Alice and Bob{\textquoteright}, Logic and Science Facing the New Technologies}, journal = {Proceedings of the 14th Congress for Logic (Nancy), Logic, Methodology and Philosophy of Science}, year = {2014}, month = {2014/01/01}, author = {Jeffrey Bub and Peter Schroeder-Heister and Gerhard Heinzmann and Wilfrid Hodges and Pierre Edouard Bour} } @article {1320, title = {Quantum Correlations and the Measurement Problem}, journal = {International Journal of Theoretical Physics}, volume = {53}, year = {2014}, month = {2013/6/30}, pages = {3346 - 3369}, abstract = { The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The {\textquoteleft}no go{\textquoteright} hidden variable theorems tell us that we can{\textquoteright}t shoe-horn correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton{\textquoteright}s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the local correlation polytope. This paper is an elaboration of these ideas, and its consequences for the measurement problem of quantum mechanics. A large part of the difficulty is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable is only apparent and depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation resolves the problem. }, doi = {10.1007/s10773-013-1695-z}, url = {http://arxiv.org/abs/1210.6371v3}, author = {Jeffrey Bub} } @article {1326, title = {Quantum Interactions with Closed Timelike Curves and Superluminal Signaling }, journal = {Physical Review A}, volume = {89}, year = {2014}, month = {2014/2/12}, abstract = { There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike separated Alice and Clio, and spacelike separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph (arXiv:1107.4675) first pointed this out for P-CTCs, but we show that Ralph{\textquoteright}s procedure for a {\textquoteright}radio to the past{\textquoteright} is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous (Proc.Roy.Soc.A, 465:631-647 (2009)) for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer. }, doi = {10.1103/PhysRevA.89.022311}, url = {http://arxiv.org/abs/1309.4751v4}, author = {Jeffrey Bub and Allen Stairs} } @article {1319, title = {Why the Tsirelson bound?}, journal = {The Probable and the Improbable: The Meaning and Role of Probability in Physics}, year = {2012}, month = {2012/08/18}, pages = {167-185}, abstract = { Wheeler{\textquoteright}s question {\textquoteright}why the quantum{\textquoteright} has two aspects: why is the world quantum and not classical, and why is it quantum rather than superquantum, i.e., why the Tsirelson bound for quantum correlations? I discuss a remarkable answer to this question proposed by Pawlowski et al (2009), who provide an information-theoretic derivation of the Tsirelson bound from a principle they call {\textquoteright}information causality.{\textquoteright} }, doi = {10.1007/978-3-642-21329-8_11}, url = {http://arxiv.org/abs/1208.3744v1}, author = {Jeffrey Bub} } @article {1325, title = {Contextuality in Quantum Mechanics: Testing the Klyachko Inequality}, year = {2010}, month = {2010/06/02}, abstract = { The Klyachko inequality is an inequality for the probabiities of the values of five observables of a spin-1 particle, which is satisfied by any noncontextual assignment of values to this set of observables, but is violated by the probabilities defined by a certain quantum state. We describe an experiment between two entangled spin-1 particles to test contextuality via a related inequality. We point out that a test of contextuality by measurements on a single particle to confirm the Klyachko inequality requires an assumption of non-disturbance by the measuring instrument, which is avoided in the two-particle experiment. }, url = {http://arxiv.org/abs/1006.0500v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1316, title = {Quantum computation and pseudo-telepathic games}, journal = {Philosophy of Science}, volume = {75}, year = {2010}, month = {2010/05/14}, pages = {458-472}, abstract = { A quantum algorithm succeeds not because the superposition principle allows {\textquoteright}the computation of all values of a function at once{\textquoteright} via {\textquoteright}quantum parallelism,{\textquoteright} but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information-processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I also introduce the notion of {\textquoteright}pseudo-telepathic{\textquoteright} games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players{\textquoteright} correlated responses in a game). }, url = {http://arxiv.org/abs/1005.2449v1}, author = {Jeffrey Bub} } @article {1315, title = {Quantum probabilities: an information-theoretic interpretation}, year = {2010}, month = {2010/05/14}, abstract = { This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that \emph{information in the physical sense has new structural features}, just as the transition from classical to relativistic physics rests on the recognition that space-time is structurally different than we thought. Hilbert space, the event space of quantum systems, is interpreted as a kinematic (i.e., pre-dynamic) framework for an indeterministic physics, in the sense that the geometric structure of Hilbert space imposes objective probabilistic or information-theoretic constraints on correlations between events, just as the geometric structure of Minkowski space in special relativity imposes spatio-temporal kinematic constraints on events. The interpretation of quantum probabilities is more subjectivist in spirit than other discussions in this book (e.g., the chapter by Timpson), insofar as the quantum state is interpreted as a credence function---a bookkeeping device for keeping track of probabilities---but it is also objective (or intersubjective), insofar as the credences specified by the quantum state are understood as uniquely determined, via Gleason{\textquoteright}s theorem, by objective correlational constraints on events in the nonclassical quantum event space defined by the subspace structure of Hilbert space. }, url = {http://arxiv.org/abs/1005.2448v1}, author = {Jeffrey Bub} } @article {1317, title = {Von Neumann{\textquoteright}s {\textquoteright}No Hidden Variables{\textquoteright} Proof: A Re-Appraisal}, journal = {Foundations of Physics}, volume = {40}, year = {2010}, month = {2010/6/11}, pages = {1333 - 1340}, abstract = { Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann{\textquoteright}s {\textquoteright}no hidden variables{\textquoteright} proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense {\textquoteright}like Bohm{\textquoteright}s theory.{\textquoteright} His seminal result provides a positive answer to the question. I argue that Bell{\textquoteright}s analysis misconstrues von Neumann{\textquoteright}s argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the {\textquoteright}beables{\textquoteright} of the theory, to use Bell{\textquoteright}s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm{\textquoteright}s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. }, doi = {10.1007/s10701-010-9480-9}, url = {http://arxiv.org/abs/1006.0499v1}, author = {Jeffrey Bub} } @article {1324, title = {Contextuality and nonlocality in {\textquoteright}no signaling{\textquoteright} theories}, journal = {Foundations of Physics}, volume = {39}, year = {2009}, month = {2009/4/21}, pages = {690 - 711}, abstract = { We define a family of {\textquoteright}no signaling{\textquoteright} bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the {\textquoteleft}no signaling{\textquoteright} polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in {\textquoteright}no signaling{\textquoteright} theories. }, doi = {10.1007/s10701-009-9307-8}, url = {http://arxiv.org/abs/0903.1462v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1323, title = {Two dogmas about quantum mechanics}, year = {2007}, month = {2007/12/27}, abstract = { We argue that the intractable part of the measurement problem -- the {\textquoteright}big{\textquoteright} measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell{\textquoteright}s assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the {\textquoteright}truthmaker{\textquoteright} for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the {\textquoteright}big{\textquoteright} measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW {\textquoteright}collapse{\textquoteright} theorists who add structure to the theory and propose dynamical solutions to the {\textquoteright}big{\textquoteright} measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events. }, url = {http://arxiv.org/abs/0712.4258v2}, author = {Jeffrey Bub and Itamar Pitowsky} } @article {1314, title = {Quantum computation from a quantum logical perspective}, year = {2006}, month = {2006/05/29}, abstract = { It is well-known that Shor{\textquoteright}s factorization algorithm, Simon{\textquoteright}s period-finding algorithm, and Deutsch{\textquoteright}s original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical perspective, the XOR algorithm appears directly as a special case of Simon{\textquoteright}s algorithm, and all three algorithms can be seen as exploiting the non-Boolean logic represented by the subspace structure of Hilbert space in a similar way. Essentially, a global property of a function (such as a period, or a disjunctive property) is encoded as a subspace in Hilbert space representing a quantum proposition, which can then be efficiently distinguished from alternative propositions, corresponding to alternative global properties, by a measurement (or sequence of measurements) that identifies the target proposition as the proposition represented by the subspace containing the final state produced by the algorithm. }, url = {http://arxiv.org/abs/quant-ph/0605243v2}, author = {Jeffrey Bub} } @article {1322, title = {Conditionalizing and commutativity: a note on Malley}, year = {2005}, month = {2005/06/19}, abstract = { This paper has been withdrawn. }, url = {http://arxiv.org/abs/quant-ph/0506159v2}, author = {Allen Stairs and Jeffrey Bub} } @article {1313, title = {Quantum information and computation}, year = {2005}, month = {2005/12/15}, abstract = { This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics. }, url = {http://arxiv.org/abs/quant-ph/0512125v2}, author = {Jeffrey Bub} } @article {1312, title = {Quantum mechanics is about quantum information}, journal = {Foundations of Physics}, volume = {35}, year = {2005}, month = {2005/04/01}, pages = {541 - 560}, abstract = { I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein{\textquoteright}s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right. }, doi = {10.1007/s10701-004-2010-x}, url = {http://arxiv.org/abs/quant-ph/0408020v2}, author = {Jeffrey Bub} } @article {1311, title = {Why the quantum?}, year = {2004}, month = {2004/02/20}, abstract = { This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information. }, url = {http://arxiv.org/abs/quant-ph/0402149v1}, author = {Jeffrey Bub} } @article {1321, title = {Can quantum cryptography imply quantum mechanics? Reply to Smolin}, year = {2003}, month = {2003/11/11}, abstract = { Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be derived from three cryptographic, or broadly information-theoretic, axioms. But Smolin disagrees, and he has given a toy theory that he claims is a counterexample. Here we show that Smolin{\textquoteright}s toy theory violates an independence condition for spacelike separated systems that was assumed in the CBH argument. We then argue that any acceptable physical theory should satisfy this independence condition. }, url = {http://arxiv.org/abs/quant-ph/0311065v1}, author = {Hans Halvorson and Jeffrey Bub} } @article {1328, title = {Characterizing quantum theory in terms of information-theoretic constraints}, journal = {Foundations of Physics}, volume = {33}, year = {2002}, month = {2003/11/01}, pages = {1561 - 1591}, abstract = { We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment--suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment. }, doi = {10.1023/A:1026056716397}, url = {http://arxiv.org/abs/quant-ph/0211089v2}, author = {Rob Clifton and Jeffrey Bub and Hans Halvorson} } @article {1310, title = {Maxwell{\textquoteright}s demon and the thermodynamics of computation}, year = {2002}, month = {2002/03/05}, abstract = { It is generally accepted, following Landauer and Bennett, that the process of measurement involves no minimum entropy cost, but the erasure of information in resetting the memory register of a computer to zero requires dissipating heat into the environment. This thesis has been challenged recently in a two-part article by Earman and Norton. I review some relevant observations in the thermodynamics of computation and argue that Earman and Norton are mistaken: there is in principle no entropy cost to the acquisition of information, but the destruction of information does involve an irreducible entropy cost. }, url = {http://arxiv.org/abs/quant-ph/0203017v1}, author = {J. Bub} } @article {1308, title = {Secure key distribution via pre- and post-selected quantum states}, journal = {Physical Review A}, volume = {63}, year = {2001}, month = {2001/2/14}, abstract = { A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described. }, doi = {10.1103/PhysRevA.63.032309}, url = {http://arxiv.org/abs/quant-ph/0006086v3}, author = {J. Bub} } @article {1309, title = {The quantum bit commitment theorem}, year = {2000}, month = {2000/07/25}, abstract = { Unconditionally secure two-party bit commitment based solely on the principles of quantum mechanics (without exploiting special relativistic signalling constraints, or principles of general relativity or thermodynamics) has been shown to be impossible, but the claim is repeatedly challenged. The quantum bit commitment theorem is reviewed here and the central conceptual point, that an {\textquoteleft}Einstein-Podolsky-Rosen{\textquoteright} attack or cheating strategy can always be applied, is clarified. The question of whether following such a cheating strategy can ever be disadvantageous to the cheater is considered and answered in the negative. There is, indeed, no loophole in the theorem. }, url = {http://arxiv.org/abs/quant-ph/0007090v4}, author = {Jeffrey Bub} } @article {1307, title = {Quantum Mechanics as a Principle Theory}, year = {1999}, month = {1999/10/22}, abstract = { I show how quantum mechanics, like the theory of relativity, can be understood as a {\textquoteright}principle theory{\textquoteright} in Einstein{\textquoteright}s sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999). }, url = {http://arxiv.org/abs/quant-ph/9910096v1}, author = {Jeffrey Bub} } @article {1327, title = {Revised Proof of the Uniqueness Theorem for {\textquoteright}No Collapse{\textquoteright} Interpretations of Quantum Mechanics }, year = {1999}, month = {1999/10/22}, abstract = { We show that the Bub-Clifton uniqueness theorem for {\textquoteright}no collapse{\textquoteright} interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the {\textquoteright}weak separability{\textquoteright} assumption. }, url = {http://arxiv.org/abs/quant-ph/9910097v1}, author = {Jeffrey Bub and Rob Clifton and Sheldon Goldstein} }