Evidence for the epistemic view of quantum states: A toy theory

Spekkens, Robert W.

doi:10.1103/physreva.75.032110

Cited by 570 publications

(872 citation statements)

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“…A second sort of worry is raised by the existence of various 'toy-theories' that satisfy the three information-theoretic constraints of the CBH characterization theorem and yet are palpably not quantum mechanics (Spekkens, 2004;Smolin, 2003). These toy theories are not counter-examples in the logical sense to the CBH theorem, as they fail to satisfy the requirements of the theorem: Halvorson and Bub (2003) argue that Smolin's toy theory exhibits physical pathologies as it violates an analogue of the C * -independence condition, and Halvorson (2004) proves that Spekkens' toy-theory is not a C * -algebraic theory.…”

Section: Some Queries Regarding the C * -Algebraic Starting Pointmentioning

confidence: 99%

Quantum Information Theory and the Foundations of Quantum Mechanics

Timpson¹

2013

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of Thesis Submitted for the Degree of Doctor of PhilosophyThis thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory;however it is maintained that in both settings 'information' functions as an abstract noun, hence does not refer to a particular or substance. The popular claim 'Information is Physical' is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske's (1981) attempt to base a semantic notion of information on ideas from information theory.The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of recognising the logical status of 'information' as an abstract noun: it is argued that the conceptual puzzles often associated with this phenomenon result from the familiar error of hypostatizing an abstract noun.The approach of Deutsch and Hayden (2000) to the questions of locality and information flow in entangled quantum systems is assessed. It is suggested that the approach suffers from an equivocation between a conservative and an ontological reading; and the differing implications of each is examined. Some results are presented on the characterization of entanglement in the Deutsch-Hayden formalism.Part I closes with a discussion of some philosophical aspects of quantum computation.In particular, it is argued against Deutsch that the Church-Turing hypothesis is not underwritten by a physical principle, the Turing Principle. Some general morals are drawn concerning the nature of quantum information theory.In Part II, attention turns to the question of the implications of quantum information theory for our understanding of the meaning of the quantum formalism. Following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.

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Section: Some Queries Regarding the C * -Algebraic Starting Pointmentioning

confidence: 99%

Quantum Information Theory and the Foundations of Quantum Mechanics

Timpson¹

2013

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“…Investigating then the difference between the first principles of a particular toy model, and of standard quantum mechanics, one learns with precision which fundamental principle is responsible for which element of the quantum theoretic structure. Spekkens's toy model, for example, accommodates such quantum phenomena as noncommutativity, interference, the multiplicity of convex decompositions of a mixed state, no cloning, teleportation, and others [52]. We learn that the continuous state space, the existence of a Bell theorem, or contextuality, all of which are absent from this toy model, go unconnected with the appearance of the phenomena that are reproduced.…”

Section: Intentionally Incomplete Reconstructionsmentioning

confidence: 99%

“…Recently, a new type of information-theoretic reconstructions appeared, intentionally not aimed at deriving the whole quantum theoretic structure [1,2,3,22,46,50,52]. Christened pejoratively by their own authors, these "toy models", "fantasy quantum mechanics," or "quantum mechanics lite" employ a methodology of reconstruction that has been overlooked by the previous generations of researchers: it is now claimed as helpful to reconstruct, not the full version but only a certain part of quantum theory.…”

Section: Intentionally Incomplete Reconstructionsmentioning

confidence: 99%

Reconstruction of Quantum Theory

Grinbaum

2007

The British Journal for the Philosophy of Science

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What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the ones due to Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.1 What is wrong with interpreting quantum mechanics?Ever since the first days of quantum mechanics physicists as well as philosophers tried to interpret it, understanding this task as a problem of giving to the new physical theory a clear meaning. One of the principal reasons why one has always felt the need for interpretations has to do with the puzzling aspect of the formalism of quantum mechanics, usually referred to as the measurement problem. Reversible unitary evolution of the wave function, according to standard quantum mechanics, at the moment of measurement is replaced by an irreversible transformation known as wavefunction collapse. First and foremost, interpretations of quantum mechanics aimed at making sense of this surprising change in the theory's dynamics, sometimes taking the collapse at face value and claiming its fundamental irreducible role, or sometimes going to another extreme and denying the collapse altogether. However, looking globally, the enterprize of interpreting quantum mechanics failed: today we still have no consensus on what the meaning of quantum theory is. None of the proposed answers has won overall acceptance. Perhaps the most remarkable manifestation of the failure to interpret quantum mechanics is the attitude taught to most young physicists in 1 lecture rooms and research laboratories in the last half century, "Shut up and calculate!" [37] Why did attempts at a univocal interpretation fail? Many answers are possible, and among them we favor two, both showing that there is an intrinsic deficiency in the idea of interpreting a physical theory with the help of philosophical instruments only.The first answer is that to a physical theory one would naturally like to give a physical meaning in the Greek sense of ϕύσις, i.e. we-as part of the physicists' audience-expect to be told a true story about nature. This is because we casually tend to apply physical theory to the phenomenal world to learn something about the latter, and not the world to physical theory in order to invent a meaning of the theory. Physical theory is above all a tool for predicting the yet unobserved phenomena; so employing existing knowledge and experience of the world to interpret physics runs counter to its basic function as a scientific theory. However, notwithstanding such an against-the-grain direction in which a philosophical interpretation operates, the former does not necessarily lead to formal contradiction that would invalidate the interpretation program logically; more modestly but perhaps no less irr...

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“…The intention is that all this construction is done in such a way as to produce, in the hiddenvariable part of the state space, an image of the formally stochastic quantum macrodynamics that is actually forward-stochastic (either at the fundamental level, as a consequence of fundamental stocasticity in the hidden-variable dynamics; or at the effective level, as a result of an appropriately-chosen initial probability distribution over the hidden variables). 16 This will be guaranteed if (i) the quantum macrostates can be characterised in terms of some dynamical variable (such as position); (ii) the hidden variables can be taken to represent the actual value of that variable; (iii) the dynamics, and the hidden variable initial probability, can be chosen to ensure that the probability of the hidden variables having some value is equal to the probability given for that value by ondly, there is a research program in foundations of quantum theory (see, e. g. , Harrigan and Spekkens (2010) and Spekkens (2007)) that tries to eliminate the quantum state entirely from hidden-variable theories. For reasons of space I omit further discussion of these approaches.…”

Section: Resolving the Measurement Problemmentioning

confidence: 99%

Probability in Physics: Stochastic, Statistical, Quantum

Wilson¹

2014

Chance and Temporal Asymmetry

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I review the role of probability in contemporary physics and the origin of probabilistic time asymmetry, beginning with the pre-quantum case (both stochastic mechanics and classical statistical mechanics) but concentrating on quantum theory. I argue that quantum mechanics radically changes the pre-quantum situation and that the philosophical nature of objective probability in physics, and of probabilistic asymmetry in time, is dependent on the correct resolution of the quantum measurement problem.

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Evidence for the epistemic view of quantum states: A toy theory

Cited by 570 publications

References 61 publications

Quantum Information Theory and the Foundations of Quantum Mechanics

Quantum Information Theory and the Foundations of Quantum Mechanics

Reconstruction of Quantum Theory

Probability in Physics: Stochastic, Statistical, Quantum

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