Commuting Operations Factorise

Does commutation imply factorisation? More precisely, consider two parties, Alice and Bob, each of whom applies an operation on a shared quantum system, K. If the order of their operations does not affect the outcomes, a natural question arises: can K be factorised into separate parts, one that is only accessible to Alice and another that is only accessible to Bob? The special case of the question, where Alice and Bob’s operations are measurements that produce classical outcomes, is known as Tsirelson’s problem. In this talk, I will present a “fully quantum” generalisation of the question and provide an answer to it in the finite-dimensional case.

This is joint work with Ramona Wolf; preprint available at arXiv:2308.05792.