The simplicial approach to quantum contextuality


Ipek, S. (2022). The simplicial approach to quantum contextuality. Perimeter Institute. https://pirsa.org/22120061


Ipek, Selman. The simplicial approach to quantum contextuality. Perimeter Institute, Dec. 15, 2022, https://pirsa.org/22120061


          @misc{ pirsa_22120061,
            doi = {10.48660/22120061},
            url = {https://pirsa.org/22120061},
            author = {Ipek, Selman},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The simplicial approach to quantum contextuality},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {dec},
            note = {PIRSA:22120061 see, \url{https://pirsa.org}}

Selman Ipek Bilkent University


Central to many of the paradoxes arising in quantum theory is that the act of measurement cannot be understood as merely revealing the pre-existing values of some hidden variables, a phenomenon known as contextuality. In the past few years quantum contextuality has been formalized in a variety of ways; operation-theoretic, sheaf-theoretic, (hyper)graph-theoretic, and cohomological. In this seminar we will discuss the simplicial approach to contextuality introduced in arXiv:2204.06648, which builds off the earlier sheaf-theoretic approach of Abramsky-Brandenberger (arXiv:1102.0264) and the cohomological approach of Okay, et al. (arXiv:1701.01888). In the simplicial approach measurement scenarios and their statistics can be modeled topologically as simplicies using the theory of simplicial sets. The connection to topology provides an additional analytical handle, allowing for a rigorous study of both state-dependent and state-independent contextuality. Using this formalism we present a novel topological proof of Fine's theorem for characterizing noncontextuality in Bell scenarios.

Zoom link:  https://pitp.zoom.us/j/93748699892?pwd=SVhVaTdoRmlwaGdCZVdIWVlKTktjQT09