QLunch: Ranyiliu Chen

Speaker: Ranyiliu Chen from QMATH

Title: All Projective Measurements Can be Self-tested

Abstract: 

In this work, we provide the first general result of self-testing all real-valued projective measurements. Specifically, we explicitly construct a self-testing protocol that incorporates any such measurement. To establish this, we adopt the post-hoc self-testing method which, based on an (established) initial self-testing strategy, infers the characterization of a new measurement from correlations. 

We first prove a sufficient condition for post-hoc self-testing. Then by applying post-hoc self-testing with an initial strategy from recent work (Mančinska et al, 2021), we construct a self-tested strategy that can always incorporate the measurement we aim to verify. In addition to that, we develop the theory of iterative post-hoc self-testing, i.e., sequential utilization of the post-hoc self-testing. Being independent of our explicit self-testing protocol construction, the theory of iterative post-hoc self-testing may be of interest to researchers seeking to create self-testing protocols from their own selected initial strategies by providing a theoretical tool for understanding self-testing. 

This is a joint work with Laura Mančinska and Jurij Volčič [arXiv.2302.00974].