Solving Large-Scale Optimization Problems Related to Bell's Theorem

Details Solving Large-Scale Optimization Problems Related to Bell's Theorem Solving Large-Scale Optimization Problems Related to Bell's Theorem

2012-04-16

arxiv.org/abs/1204.3587v1

Physics

Quantum Physics

19 pages, 7 tables, 1 figure

Scientific paper

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve problems which are orders of magnitude larger. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.

Affiliated with

Also associated with

No associations

Rating

Solving Large-Scale Optimization Problems Related to Bell's Theorem 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 Solving Large-Scale Optimization Problems Related to Bell's Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solving Large-Scale Optimization Problems Related to Bell's Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-7265