Video URL
https://pirsa.org/16100034Tsirelson's problem and linear system games
APA
(2016). Tsirelson's problem and linear system games. Perimeter Institute for Theoretical Physics. https://pirsa.org/16100034
MLA
Tsirelson's problem and linear system games. Perimeter Institute for Theoretical Physics, Oct. 18, 2016, https://pirsa.org/16100034
BibTex
@misc{ scivideos_PIRSA:16100034, doi = {10.48660/16100034}, url = {https://pirsa.org/16100034}, author = {}, keywords = {Quantum Foundations}, language = {en}, title = {Tsirelson{\textquoteright}s problem and linear system games}, publisher = {Perimeter Institute for Theoretical Physics}, year = {2016}, month = {oct}, note = {PIRSA:16100034 see, \url{https://scivideos.org/index.php/pirsa/16100034}} }
Abstract
In quantum information, we frequently consider (for instance, whenever we talk about entanglement) a composite system consisting of two separated subsystems. A standard axiom of quantum mechanics states that a composite system can be modeled as the tensor product of the two subsystems. However, there is another less restrictive way to model a composite system, which is used in quantum field theory: we can require only that the algebras of observables for each subsystem commute within some larger subalgebra. For finite-dimensional systems, these two axioms are equivalent, but this is not necessarily true for infinite-dimensional systems. Tsirelson's question (which comes in several variants) asks whether the correlations arising from commuting-operator models can always be represented by tensor-product models. I will give examples of linear system non-local games which cannot be played perfectly with tensor-product strategies, but can be played perfectly with commuting-operator strategies, resolving (one version of) Tsirelson's question in the negative. From these examples, we can also derive other consequences for the theory of non-local games, such as the undecidability of determining whether a non-local game has a perfect quantum strategy.