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Title: The quantum measurement problem and physical reality: A computation theoretic perspective
Authors: Srikanth, R.
Keywords: quantum computation,
complexity theory
quantum measurement problem
Issue Date: Dec-2006
Publisher: American Institute of Physics
Citation: AIP Conference Proceedings Vol.864 on Quantum Computing, 2006, p178-193
Abstract: Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete subphysical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.
Description: Paper presented at the AIP Conference Proceedings Vol.864 on Quantum Computation: Back Action, Edited by D. Goswami, held at IIT Kanpur, March 5-12, 2006. Open Access.
ISBN: 0735403627
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Copyright: (2006) by American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Appears in Collections:Research Papers (LAMP)

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