Probabilities for Observing Mixed Quantum States given Limited Prior Information

The original development of the formalism of quantum mechanics involved the study of isolated quantum systems in pure states. Such systems fail to capture important aspects of the warm, wet, and noisy physical world which can better be modelled by quantum statistical mechanics and local quantum field theory using mixed states of continuous systems. In this context, we need to be able to compute quantum probabilities given only partial information. Specifically, suppose that B is a set of operators. This set need not be a von Neumann algebra. Simple axioms are proposed which allow us to identify a function which can be interpreted as the probability, per unit trial of the information specified by B, of observing the (mixed) state of the world restricted to B to be σ when we are given ρ – the restriction to B of a prior state. This probability generalizes the idea of a mixed state (ρ) as being a sum of terms (σ) weighted by probabilities. The unique function satisfying the axioms can be defined in terms of the relative entropy. The analogous inference problem in classical probability would be a situation where we have some information about the prior distribution, but not enough to determine it uniquely. In such a situation in quantum theory, because only what we observe should be taken to be specified, it is not appropriate to assume the existence of a fixed, definite, unknown prior state, beyond the set B about which we have information. The theory was developed for the purposes of a fairly radical attack on the interpretation of quantum theory, involving many-worlds ideas and the abstract characterization of observers as finite information-processing structures, but deals with quantum inference problems of broad generality
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Translate to english
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,780
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
A Priori Probability and Localized Observers.Matthew Donald - 1992 - Foundations of Physics 22 (9):1111-1172.
Quantum Information Processing, Operational Quantum Logic, Convexity, and the Foundations of Physics.Howard Barnum - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):343-379.
Quantum Information Does Not Exist.Armond Duwell - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):479-499.
Negative and Complex Probability in Quantum Information.Vasil Penchev - 2012 - Philosophical Alternatives (1):63-77.
Bohmian Mechanics and Quantum Information.Sheldon Goldstein - 2010 - Foundations of Physics 40 (4):335-355.
Quantum Probability and Many Worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
EPR-Experiment Explanation.Ivan Z. Tsekhmistro - 2007 - The Proceedings of the Twenty-First World Congress of Philosophy 5:95-99.
Added to PP index

Total downloads
16 ( #331,465 of 2,214,632 )

Recent downloads (6 months)
1 ( #408,824 of 2,214,632 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature