Hiding bits in Bell states

Abstract

We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in $n$, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.

4 pages RevTex, 1 figure, various small changes and additional paragraph on optics implementation

References in corpus (3)

• On the Theory of Quantum Secret Sharing
• Entanglement Measures under Symmetry
• Local Distinguishability of Multipartite Orthogonal Quantum States

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