Bound Secrecy and Bound Entanglement: Where (Qu)Bits Go to Die

Abstract: There is a surprising result in information theory where the quantum version of a conjecture is known to be true, and the classical one remains open. The conjecture is that there exists a joint probability distribution for three parties, Alice, Bob, and Eve, that exhibits bound secrecy. Simply put, bound secrecy is the idea that there can secret information present in the correlations of the random variables belonging to Alice and Bob but that is completely unknown to Eve, and yet despite this, no matter what Alice and Bob say to each other publicly, they will be unable to distill any bits of a secret key, random bits completely unknown to Eve. This is a very surprising fact, as it seems that there is a secret that Alice and Bob share and yet cannot access despite their best efforts. The quantum version of this conjecture states that there exist joint states for Alice and Bob which are entangled and therefore cannot be created without spending some amount of entanglement, but from which no pure entangled states, such as Bell pairs, can be distilled. These joint states are called bound entangled, and not only are they known to exist, some small examples have been found.

Computer scienceMathematicsPhysics

Audience: researchers in the topic

MIT Simple Person's Applied Mathematics Seminar