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 NP-complete problems (often brute-force 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.

arXiv comment11 pages

References in corpus (9)

• Ising formulations of many NP problems
• The information paradox: A pedagogical introduction
• Better Late than Never: Information Retrieval from Black Holes
• Black hole evaporation: A paradigm
• Sign- and magnitude-tunable coupler for superconducting flux qubits
• A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence
• Do Black Holes Destroy Information?
• Realistic clocks, universal decoherence and the black hole information paradox
• Benefits of Objective Collapse Models for Cosmology and Quantum Gravity