Apr 17 – 21, 2023
Perimeter Institute for Theoretical Physics
America/Toronto timezone

Is causal optimization polynomial optimization?

Apr 20, 2023, 9:30 AM
PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

PI/4-405 - Bob Room

Perimeter Institute for Theoretical Physics



David Gross (University of Cologne)


"Is there a complete semi-definite programming hierarchy for quantum causal problems? We divide the question into two parts. First: Can quantum causal problems be expressed as polynomial optimization problems (this talk). Second: Can this class of polynomial optimizations be solved by means of SDPs (Laurens' talk). The optimizations we consider here are ""polynomial"" in two ways. They are over the unknown observable algebra of the hidden systems, which are specified by non-commutative polynomials in a set of generators. But they also involve independence constraints, which are commutative polynomials in the state. A hierarchy
of such polynomial tests is complete if one can construct a quantum model for any observed distribution that passes all of them. We've recently had some success in finding such constructions, but also ran into problems in the general case [1, 2]. I give a high-level presentation of the state of the play.

[1] https://arxiv.org/abs/2110.14659
[2] https://arxiv.org/abs/2212.11299"

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