The Quantum Measurement Problem and Physical reality: A Computation Theoretic Perspective

Srikanth, R.

doi:10.1063/1.2400889

Cited by 7 publications

(13 citation statements)

References 42 publications

(68 reference statements)

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“…Since, as noted earlier, the coin makes the walk reversible, we have the interesting scenario that the relativistic causal structure is fundamentally a consequence of conservation of information. This is in accordance with some recent works that have studied possible information theoretical bases for the mathematical structure of quantum mechanics [39][40][41][42].…”

Section: A Decoupled Discrete-time Quantum Walk Equation In Klein-gosupporting

confidence: 92%

Relationship between quantum walks and relativistic quantum mechanics

2010

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Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrödinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, the maximum speed the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended. * Electronic address: cmadaiah@iqc.ca † Electronic address: subhashish@cmi.ac.in ‡ Electronic address: srik@poornaprajna.org

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Section: A Decoupled Discrete-time Quantum Walk Equation In Klein-gosupporting

confidence: 92%

Relationship between quantum walks and relativistic quantum mechanics

2010

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“…The Church-Turing thesis of computer science [22] may then be invoked to suggest that no physical process, interpreted as a procedure for computing a function, can be more powerful than Turing machines. Thus the incompleteness of physics could manifest in the physical uncomputability of Turing uncomputable problems [46].…”

Section: B Bhip Viewed As An Inconsistent Self-reference In Quantum G...mentioning

confidence: 99%

Gödel incompleteness and the black hole information paradox

Srikanth

Hebri²

2008

Quantum Inf Process

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Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization is to identify the Gödel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.

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“…In Ref. [8], we speculate that this scale is related to a discretization of Hilbert space. This approach provides a possible computation theoretic resolution to the quantum measurement problem.…”

Section: Introductionmentioning

confidence: 95%

“…Other recent related works that have studied the computational power of variants of standard physical theories from a complexity or computability perspective are, respectively, Refs. [8,[13][14][15][16] and Refs. [8,13].…”

Section: Introductionmentioning

confidence: 99%

Entanglement, intractability and no-signaling

Srikanth¹

2010

Phys. Scr.

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We consider the problem of deriving the no-signaling condition from the assumption that, as seen from a complexity theoretic perspective, the universe is not an exponential place. A fact that disallows such a derivation is the existence of polynomial superluminal gates, hypothetical primitive operations that enable superluminal signaling but not the efficient solution of intractable problems. It therefore follows, if this assumption is a basic principle of physics, either that it must be supplemented with additional assumptions to prohibit such gates, or, improbably, that no-signaling is not a universal condition. Yet, a gate of this kind is possibly implicit, though not recognized as such, in a decade-old quantum optical experiment involving position-momentum entangled photons. Here we describe a feasible modified version of the experiment that appears to explicitly demonstrate the action of this gate. Some obvious counter-claims are shown to be invalid. We believe that the unexpected possibility of polynomial superluminal operations arises because some practically measured quantum optical quantities are not describable as standard quantum mechanical observables.

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The Quantum Measurement Problem and Physical reality: A Computation Theoretic Perspective

Cited by 7 publications

References 42 publications

Relationship between quantum walks and relativistic quantum mechanics

Relationship between quantum walks and relativistic quantum mechanics

Gödel incompleteness and the black hole information paradox

Entanglement, intractability and no-signaling

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