Entanglement enhances security in quantum communication

Secret sharing is a protocol in which a "boss" wants to send a classical message secretly to two "subordinates," such that none of the subordinates is able to know the message alone, while they can find it if they cooperate. Quantum mechanics is known to allow for such a possibility. We analyze tolerable quantum bit error rates in such secret sharing protocols in the physically relevant case when the eavesdropping is local with respect to the two channels of information transfer from the boss to the two subordinates. We find that using entangled encoding states is advantageous to legitimate users of the protocol. We therefore find that entanglement is useful for secure quantum communication. We also find that bound entangled states with positive partial transpose are not useful as a local eavesdropping resource. Moreover, we provide a criterion for security in secret sharing-a parallel of the Csiszar-Korner criterion in single-receiver classical cryptography.