ANALYSIS SEMINAR
Title：A mathematics foundation of self-testing: lifting common assumptions
Speaker:Ranyiliu Chen（University of Copenhagen）
Time: Wednesday, December13, 2023, 14:30-16:00
Venue: Mingde Building B201-1
Zoom ID: 945 2536 6360, Password: 461559
Abstract: Self-testing allows a classical verifier to infer a quantum mechanical description of untrusted quantum devices that she interacts with in a black-box manner. Somewhat contrary to the black-box paradigm, existing self-testing results tend to presuppose conditions that constrain the operation of the untrusted devices. A common assumption is that these devices perform a projective measurement of a pure quantum state. Naturally, in the absence of any prior knowledge it would be appropriate to model these devices as measuring a mixed state using POVM measurements, since the purifying/dilating spaces could be held by the environment or an adversary.
We prove a general theorem allowing to remove these assumptions, thereby promoting most existing self-testing results to their assumption-free variants. On the other hand, we pin-point situations where assumptions cannot be lifted without loss of generality. As a key (counter)example we identify a quantum correlation which is a self-test only if certain assumptions are made. Remarkably, this is also the first example of a correlation that cannot be implemented using projective measurements on a bipartite state of full Schmidt rank.
More information about the Analysis Seminar can be found here.
