Think of a communication scenario where one party, Alice, prepares D-dimensional states that another party, Bob, probes. In such a prepare-and-measure scenario, we prove that any set of pure states {ψi}i=1M and any set of extreme POVMs {Qj}j=1N can be jointly and robustly self-tested. That is: there exists a linear function f, acting on the vector P of measurement probabilities, such that f(P) is close to its maximum value iff the underlying quantum states and measurements generating P are close in trace (resp., operator) norm to the reference states and POVMs, modulo a unitary or an anti-unitary transformation. The proof requires a generalization of Wigner’s theorem, a fundamental result in particle physics that characterizes the structure of physical symmetries. The robustness analysis combines ideas from quantum state discrimination and exactly soluble models.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Analytical and Combinatorial Methods in Quantum Information Theory II.
