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

SDP approaches for quantum polynomial optimization

Apr 20, 2023, 10:00 AM
30m
PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

PI/4-405 - Bob Room

Perimeter Institute for Theoretical Physics

60

Speaker

Laurens Ligthart (University of Cologne)

Description

"Many relevant tasks in Quantum Information processing can be expressed as polynomial optimization problems over states and operators. In the earlier talk by David, we saw that this is also the case for certain (quantum) causal compatibility and causal optimization problems.
This talk will focus on several closely related semidefinite programming (SDP) hierarchies that have recently been shown to be complete for such polynomial optimization problems [arxiv:2110.14659, 2212.11299, 2301.12513]. We give a high-level overview of the techniques and mathematics that are needed for proving such statements. In particular, we will see a version of a Quantum De Finetti theorem, as well as a sketch of a constructive proof of convergence for the SDP hierarchies. Afterwards, these results are linked back to the causal compatibility problem to conclude that such SDP hierarchies are complete for a certain type of causal structures known as tree networks."

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External references