How to hide a secret direction

Abstract

We present a procedure to share a secret spatial direction in the absence of a common reference frame using a multipartite quantum state. The procedure guarantees that the parties can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. As a by-product we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N/2 and N/2-1 in a system of N elementary spins.

4 pages, 1 figure

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Classical and quantum communication without a shared reference frame
• From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Multiparty data hiding of quantum information