The Hilbertian Tensor Norm and Entangled Two-Prover Games

Details The Hilbertian Tensor Norm and Entangled Two-Prover Games The Hilbertian Tensor Norm and Entangled Two-Prover Games

2010-08-11

arxiv.org/abs/1008.1948v3

New J. Phys. 13, 043002 (2011)

Physics

Quantum Physics

33 pages, some of the results have been obtained independently in arXiv:1007.3043v2, v2: an error in Theorem 4 has been correc

Scientific paper

10.1088/1367-2630/13/4/043002

We study tensor norms over Banach spaces and their relations to quantum information theory, in particular their connection with two-prover games. We consider a version of the Hilbertian tensor norm $\gamma_2$ and its dual $\gamma_2^*$ that allow us to consider games with arbitrary output alphabet sizes. We establish direct-product theorems and prove a generalized Grothendieck inequality for these tensor norms. Furthermore, we investigate the connection between the Hilbertian tensor norm and the set of quantum probability distributions, and show two applications to quantum information theory: firstly, we give an alternative proof of the perfect parallel repetition theorem for entangled XOR games; and secondly, we prove a new upper bound on the ratio between the entangled and the classical value of two-prover games.

Affiliated with

Also associated with

No associations

Rating

The Hilbertian Tensor Norm and Entangled Two-Prover Games 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 The Hilbertian Tensor Norm and Entangled Two-Prover Games, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Hilbertian Tensor Norm and Entangled Two-Prover Games will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-480474