Measurability and Computability

1998/09/16 by Masanao Ozawa, Ozawa, Masanao · 2 citations
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9809048

8 pages, RevTeX

arxiv created 1998/09/16 · arxiv updated 2009/12/01

Abstract

The conceptual relation between the measurability of quantum mechanical observables and the computability of numerical functions is re-examined. A new formulation is given for the notion of measurability with finite precision in order to reconcile the conflict alleged by M. A. Nielsen [Phys. Rev. Lett. 79, 2915 (1997)] that the measurability of a certain observable contradicts the Church-Turing thesis. It is argued that any function computable by a quantum algorithm is a recursive function obeying the Church-Turing thesis, whereas any observable can be measured in principle.

Cited by

• Measurement-Based Quantum Turing Machines and Questions of Universalities
• Quantum Domain Theory - Definitions and Applications

Related

• Computable Functions, the Church-Turing Thesis and the Quantum Measurement Problem
• Quantum Principles and Mathematical Computability
• On Measurement and Computation
• Quantum theory, the Church–Turing principle and the universal quantum computer
• Observability and Computability in Physical Systems