Quantum information processing, operational quantum logic, convexity, and the foundations of physics


Abstract
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform on a system: ''operational states.'' I discuss general frameworks for ''operational theories'' (sets of possible operational states of a system), in which convexity plays key role. The main technical content of the paper is in a theorem that any such theory naturally gives rise to a ''weak effect algebra'' when outcomes having the same probability in all states are identified and in the introduction of a notion of ''operation algebra'' that also takes account of sequential and conditional operations. Such frameworks are appropriate for investigating what things look like from an ''inside view,'' i.e., for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ''geometric'' picture (''outside view'') coordinating them all can be had, even if this picture is very different in structure from the perspectives within it, is the key to whether we may be able to achieve a unified, ''objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ''geometric'' conception of physics.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/s1355-2198(03)00033-9
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 45,461
Through your library

References found in this work BETA

Quantum Theory of Probability and Decisions.David Deutsch - 1999 - Proceedings of the Royal Society of London:3129--37.
Entanglement and Open Systems in Algebraic Quantum Field Theory.Rob Clifton & Hans Halvorson - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (1):1-31.
Effect Algebras and Unsharp Quantum Logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.

View all 12 references / Add more references

Citations of this work BETA

Philosophy of Physics.Elise M. Crull - 2013 - Analysis 73 (4):771-784.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
82 ( #104,817 of 2,280,387 )

Recent downloads (6 months)
13 ( #62,459 of 2,280,387 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature