Hiding bits in Bell states
Abstract
The protection of a secret by sharing it, that is, by apportioning the secret data among two or more parties so that the data only become intelligible as a consequence of their cooperative action, is an important capability in modern information processing. Here we give a method of using particular quantum states to share a secret between two parties (Alice and Bob), in which the data is hidden in a fundamentally stronger way than is possible in any classical scheme. We prove that even if Alice and Bob can communicate via a classical channel, they can obtain no more than arbitrarily little information about the hidden data. They can unlock the secret only by joint quantum measurements, which require either a quantum channel, shared quantum entanglement, or direct interaction between them. We show that the creation of these secret shares can be done with just a small expenditure of quantum entanglement: less than one Einstein-Podolsky-Rosen pair per secret bit shared. The extent to which quantum states can hide shared data can be viewed as a new information-theoretic characterization of the quantum nonlocality of these states.Keywords
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