The quantum measurement problem and physical reality: a computation theoretic perspective

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 sub-physical 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.Comment: Talk presented at "Quantum Computing: Back Action 2006", IIT Kanpur, India, March 200

Entanglement, intractability and no-signaling

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 {\em 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.Comment: 17 pages, 2 figures (REVTeX 4