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NPcomplete problems and physical reality
 ACM SIGACT News Complexity Theory Column, March. ECCC
, 2005
"... Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Mal ..."
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Can NPcomplete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantummechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, MalamentHogarth spacetimes, quantum gravity, closed timelike curves, and “anthropic computing. ” The section on soap bubbles even includes some “experimental ” results. While I do not believe that any of the proposals will let us solve NPcomplete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics. 1
Quantum Information Theory and the Foundations of Quantum Mechanics
, 2004
"... This 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 ..."
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This 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; 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
Why the Quantum?
, 2004
"... This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of informa ..."
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Cited by 25 (1 self)
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This paper is a commentary on the foundational significance of the CliftonBubHalvorson theorem characterizing quantum theory in terms of three informationtheoretic constraints. 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 informationtheoretic 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 informationtheoretic 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.
De BroglieBohm PilotWave Theory: Many Worlds in Denial?
, 811
"... We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilotwave theory of de Broglie and Bohm is really a manyworlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilotwave theory does contain an ontological pilot wave (a complexvalued field in c ..."
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We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilotwave theory of de Broglie and Bohm is really a manyworlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilotwave theory does contain an ontological pilot wave (a complexvalued field in configuration space), we show that such claims arise from not interpreting pilotwave theory on its own terms. Specifically, the theory has its own (‘subquantum’) theory of measurement, and in general describes a ‘nonequilibrium ’ state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de BroglieBohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilotwave theory itself, many worlds are an illusion. It is further argued that, even leaving pilotwave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be
Signallocality and subquantum information in deterministic hiddenvariable theories
 NonLocality and Modality, volume 64 of NATO Science Series: II
"... It is proven that any deterministic hiddenvariables theory, that reproduces quantum theory for a ‘quantum equilibrium ’ distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical ‘nonequilibrium ensembles’. This ‘signallocality t ..."
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It is proven that any deterministic hiddenvariables theory, that reproduces quantum theory for a ‘quantum equilibrium ’ distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical ‘nonequilibrium ensembles’. This ‘signallocality theorem ’ generalises yet another feature of the pilotwave theory of de Broglie and Bohm, for which it is already known that signallocality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the ‘degree of nonlocality ’ of the singlet state, defined as the (equilibrium) fraction of outcomes at one wing of an EPRexperiment that change in response to a shift in the distant angular setting. It is shown by explicit calculation that these bounds are satisfied by pilotwave theory. The degree of nonlocality is interpreted as the average number of bits of ‘subquantum information ’ transmitted superluminally, for an equilibrium ensemble. It is proposed that this quantity might provide a novel measure of the entanglement of a quantum state, and that the field of quantum information would benefit from a more explicit hiddenvariables approach. It is argued that the signallocality theorem supports the hypothesis, made elsewhere, that in the remote past the universe relaxed to a state of statistical equilibrium at the hiddenvariable level, a state in which nonlocality happens to be masked by quantum noise. 1To appear in: Modality, Probability, and Bell’s Theorems, eds. T. Placek and J. Butterfield
Hidden Variables and the LargeScale Structure of Spacetime
, 2005
"... We discuss how to embed quantum nonlocality in an approximately classical spacetime background, a question which must be answered irrespective of any underlying microscopic theory of spacetime. We argue that, in deterministic hiddenvariables theories, the choice of spacetime kinematics should be di ..."
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We discuss how to embed quantum nonlocality in an approximately classical spacetime background, a question which must be answered irrespective of any underlying microscopic theory of spacetime. We argue that, in deterministic hiddenvariables theories, the choice of spacetime kinematics should be dictated by the properties of generic nonequilibrium states, which allow nonlocal signalling. Such signalling provides an operational definition of absolute simultaneity, which may naturally be associated with a preferred foliation of classical spacetime. The argument applies to any deterministic hiddenvariables theory, and to both flat and curved spacetime backgrounds. We include some critical discussion of Einstein’s 1905 ‘operational ’ approach to relativity, and compare it with that of Poincaré.
Generalizations of Quantum Mechanics
, 2005
"... We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hiddenvariables theories (such as the pilotwave model) and their extension to “quantum nonequilibrium, ” and we consider the continu ..."
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We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hiddenvariables theories (such as the pilotwave model) and their extension to “quantum nonequilibrium, ” and we consider the continuous spontaneous localization model of wave function collapse. Other models are briefly discussed.
2004b) ”Extreme test of quantum theory with black holes,” astroph/0412503
"... We propose an extreme test of quantum theory using astrophysical black holes and entangled photons from atomic cascades. The identification of a cascade emission close to a blackhole event horizon would allow us to observe photons entangled with partners that have fallen behind the horizon. The exp ..."
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We propose an extreme test of quantum theory using astrophysical black holes and entangled photons from atomic cascades. The identification of a cascade emission close to a blackhole event horizon would allow us to observe photons entangled with partners that have fallen behind the horizon. The experiment involves testing the characteristic cos 2 Θ modulation of photon transmission through a pair of polarisers at relative angle Θ (Malus ’ law). For single photons, Malus ’ law is a remarkable feature of quantum theory: it is equivalent to expectation additivity for incompatible observables, and is generically violated for hiddenvariables theories with nonstandard probability distributions. An experiment with entangled states straddling an event horizon is motivated by the Hawking information loss puzzle, as well as on general grounds. In principle, one could test the currently observed Xray photons in iron lines from blackhole accretion discs. However, only a small fraction ( ∼ 0.6%) have cascade partners, and current Xray polarimetry does not permit successive measurements on a single Xray photon. A realisable experiment requires the identification of an
2004), Quantum computing and hidden variables I: mapping unitary to stochastic matrices
"... This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hiddenvariable theory satisfying a reasonable axiom called “indifference to the ident ..."
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This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hiddenvariable theory satisfying a reasonable axiom called “indifference to the identity, ” we could solve the Graph Isomorphism and Approximate Shortest Vector problems in polynomial time, as well as an oracle problem that is known to require quantum exponential time. We could also search an Nitem database using O ( N1/3) queries, as opposed to O ( N1/2) queries with Grover’s search algorithm. On the other hand, the N1/3 bound is optimal, meaning that we could probably not solve NPcomplete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model. 1