01278nas a2200157 4500008004100000245003500041210003500076300000800111490000600119520082700125100001700952700002200969700002800991700002401019856007701043 2007 eng d00aHow to hide a secret direction0 aHow to hide a secret direction a2440 v93 aWe 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.1 aBagan, Emili1 aCalsamiglia, John1 aDemkowicz-Dobrzanski, R1 aMuĂ±oz-Tapia, Ramon uhttp://iopscience.iop.org/1367-2630/9/8/244/pdf/1367-2630\_9\_8\_244.pdf