Entropic Geometry from Logic

Details Entropic Geometry from Logic Entropic Geometry from Logic

2002-12-10

arxiv.org/abs/quant-ph/0212065v3

ENTCS - MFPS 2003

Physics

Quantum Physics

19 pages, 8 figures

Scientific paper

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic + Partiality of Knowledge + Entropy. That is: 1. A finitary probability space \Delta^n (=all probability measures on {1,...,n}) can be fully and faithfully represented by the pair consisting of the abstraction D^n (=the object up to isomorphism) of a partially ordered set (\Delta^n,\sqsubseteq), and, Shannon entropy; 2. D^n itself can be obtained via a systematic purely order-theoretic procedure (which embodies introduction of partiality of knowledge) on an (algebraic) logic. This procedure applies to any poset A; D_A\cong(\Delta^n,\sqsubseteq) when A is the n-element powerset and D_A\cong(\Omega^n,\sqsubseteq), the domain of mixed quantum states, when A is the lattice of subspaces of a Hilbert space. (We refer to http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-02-07.html for a domain-theoretic context providing the notions of approximation and content.)

Affiliated with

Also associated with

No associations

Rating

Entropic Geometry from Logic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entropic Geometry from Logic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entropic Geometry from Logic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-638212