QLunch: Nicholas Gauguin Houghton-Larsen

Speaker: Nicholas Gauguin Houghton-Larsen from QMATH

Title: A New Perspective on Quantum Self-Testing

Abstract: Imagine we interact with two computing devices, each accepting one of $n$ inputs and producing one of $m$ outputs in return. Assume they work by locally performing one of $n$ possible $m$-outcome measurements on a shared quantum state. Can the state and measurements be deduced from the probabilistic input-output behaviour?

There is always more than one state-measurement configuration producing a given behaviour, since e.g. a local unitary rotation of state and measurements leaves the behaviour invariant. For some behaviours, however, the configuration can be deduced “up to certain transformations”. This phenomenon is known as quantum self-testing, and has theoretical as well as practical implications.
Whereas the standard “up to certain transformations”-definition is mathematically unambiguous, its operational meaning is unclear (for example, it is not obvious how to formulate it in a theory different from quantum theory). In this talk I will recast the definition operationally in terms of side-computations the devices can secretly perform during our interaction with them. Formally, I provide a connection between state-measurement configurations and maximal* elements of a pre-order of side-computations. Self-testing is essentially the existence of a greatest* element.
Along the way I present a few results of independent interest.