PhD Defense Ranyiliu Chen
Title: Black-box protocols for certification of quantum devices
Abstract:
While the Born’s rule allows us to predict the output statistics of quantum devices, inferring the underlying quantum functionality from these statistics without any prior knowledge of the device is generally difficult. Intriguingly, this challenge can be overcome by self-testing, a phenomenon where certain non-local statistics is exclusively produced by certain configuration of the devices.
This thesis contributes to a refined mathematical framework of self-testing from three aspects. First, via a detailed analysis of Naimark dilation, restriction, and purification transformations within non-local strategies we systematically remove the common assumptions under natural conditions. We can eliminate assumptions of purity, full-rankness, and projectivity, thereby lifting many existing self-testing protocols to their strongest form. We further identify specific instances where these assumptions remain necessary, by identifying a statistic that admit no pure, full-rank projective realization. A no-go result shows non-projective measurements can never be self-tested in the strongest sense.
Second, we delve into the issue of complex conjugate, refining the formulation of complex local dilation and complex self-testing where the definition of self-testing is relaxed to allow complex conjugation. A conjecture on the operator-algebraic structure of complex self-testing is proposed. Additionally, we revisit the notion of “reality” in quantum strategies, examining what it means for a strategy to be “real” and addressing subtleties within this concept. Lastly, we introduce the first robust, assumption-free self-testing protocol applicable to any real projective measurement. This is achieved through a new theoretical method, posthoc
self-testing, which enables construction of self-tests from established ones. We further generalise this method in an iterative manner, paving the way for future developments in self-testing protocols across different classes of measurements.
Supervisor: Laura Mančinska, Københavns Universitet
Assessment Committee:
Albert H. Werner (chair), Københavns Universitet
Antonio Acín, ICFO-Institut de Ciencies Fotoniques
Remigiusz Augusiak, Polish Academy of Sciences