A Connection Between Gentle Measurement of Quantum States and Differential Privacy
I'll explain a surprising new connection between, on the one hand, gentle measurement (where one wants to measure n unentangled quantum states, in a way that damages the states only by a little), and on the other hand, differential privacy (a field of classical CS where one wants to query a database about n users, in a way that reveals only a little about any individual user). The connection is bidirectional, though with loss of parameters in going from DP to gentle measurement (the nontrivial direction). By exploiting this connection, together with recent results from classical DP, we're able to give a new protocol for so-called "shadow tomography" of quantum states, which improves over the parameters of my previous protocol for that task, and which has the additional advantage of being "online" (that is, the measurements are processed and responded to one at a time).
Joint work with Guy Rothblum (Weizmann Institute); paper still in preparation.