No-go for quantum seals

Authors note: After posting this manuscript, we were made aware of a number of previous works along very similar lines, such as Refs [1-5] in version 2 of this manuscript, amongst others. We had formulated this concept and arrived at our results independently, and regret that as a result we did not properly cite these works and failed to put our work in a proper context. We are grateful to the individuals who brought this to our attention, and we are gratified to find that our ideas, while not as new as we had believed, are at least of interest to the community. We are currently working on assessing how our results relate to these prior works. In the mean time, we remain proud of our work, and we present the manuscript in its original form. Original abstract: We introduce the concept of a quantum "seal" and investigate its feasibility. We define a seal as a state provided by Alice to Bob along with a set of instructions which Bob can follow in order to "break the seal" and read the classical message stored inside. We define two success criteria for a seal: the probability Bob can successfully read the message if he follows Alice's instructions without any further input 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 prove that within the constraints of quantum mechanics these two criteria are mutually exclusive. Finally, we derive upper and lower bounds on the achievability of a probabilistic seal for various message lengths, and show that for a 1-bit message our bound is tight.