The Computational Limit to Quantum Determinism and the Black Hole Information Loss Paradox
Abstract
The present paper scrutinizes the principle of quantum determinism, which maintains that the complete information about the initial quantum state of a physical system should determine the system's quantum state at any other time. As it shown in the paper, assuming the strong exponential time hypothesis, SETH, which conjectures that known algorithms for solving computational NPcomplete problems (often bruteforce algorithms) are optimal, the quantum deterministic principle cannot be used generally, i.e., for randomly selected physical systems, particularly macroscopic systems. In other words, even if the initial quantum state of an arbitrary system were precisely known, as long as SETH is true it might be impossible in the real world to predict the system's exact final quantum state. The paper suggests that the breakdown of quantum determinism in a process, in which a black hole forms and then completely evaporates, might actually be physical evidence supporting SETH.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.7234
 Bibcode:
 2014arXiv1412.7234B
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 11 pages