PIRSA:16100034

Tsirelson's problem and linear system games

(2016). Tsirelson's problem and linear system games. Perimeter Institute. https://pirsa.org/16100034

Tsirelson's problem and linear system games. Perimeter Institute, Oct. 18, 2016, https://pirsa.org/16100034 

          @misc{ pirsa_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},
            year = {2016},
            month = {oct},
            note = {PIRSA:16100034 see, \url{https://pirsa.org}}
          }
DOI 10.48660/16100034
Collection
Talk Type Scientific Series
Subject

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.