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)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
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.H. Barnum - 2003 - Studies in History and Philosophy of Science Part B 34 (3):343-379.
Quantum Information Does Not Exist.A. Duwell - 2003 - Studies in History and Philosophy of Science Part B 34 (3):479-499.
Negative and Complex Probability in Quantum Information.Vasil Penchev - 2012 - Philosophical Alternatives (1):63-77.
A Probabilistic Approach to Quantum Mechanics Based on Tomograms.Michele Caponigro, Stefano Mancini & Vladimir I. Man'ko - unknown
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 38 (2):333-350.
Popper's Propensity Interpretation and Heisenberg's Potentia Interpretation.Ravi V. Gomatam - unknown
Explaining the Unobserved: Why Quantum Theory Ain't Only About Information.Amit Hagar & Meir Hemmo - 2006 - Foundations of Physics 36 (9):1295-1234.
Added to index2010-09-17
Total downloads16 ( #296,273 of 2,163,974 )
Recent downloads (6 months)1 ( #348,017 of 2,163,974 )
How can I increase my downloads?