No-Go Bounds for Quantum Seals

We investigate the feasibility of quantum seals. A quantum seal is a state provided by Alice to Bob along with information which Bob can use to make a measurement, "break the seal," and read the classical message stored inside. There are two success criteria for a seal: the probability Bob can successfully read the message without any further information from Alice must be high, and if Alice asks for the state back from Bob, the probability Alice can tell if Bob broke the seal without permission must be high. We build on the work of [Chau, PRA 2007], which gave optimal bounds on these criteria, showing that they are mutually exclusive for high probability. We weaken the assumptions of this previous work by providing Bob with only a classical description of a prescribed measurement, rather than classical descriptions of the possible seal states. We show that this weakening does not affect the bounds but does simplify the analysis. We also prove upper and lower bounds on an alternative operational metric for measuring the success criteria.