Multipartite quantum steering and cryptographical application

Recently, the concept of genuine N-partite Einstein-Podolsky-Rosen (EPR) steering has been developed [1], which is the natural multipartite extension of the original EPR paradox. Useful properties emerged from those special quantum states are not guaranteed for multipartite entangled states. And then a related concept of collective EPR steering in multipartite systems has been introduced, where the quantum state of a given mode can only be steered collectively by a group of other modes, but not by any individual of them [2]. This feature thus opens the possibility for the realization of more secure multimode quantum cryptography, such as quantum secret sharing (QSS). QSS aims at protecting a highly important message, by demanding that all receivers must collaborate to decrypt the secret sent by the sender. Unlike the conventional QSS protocols, the usage of the collective steering as quantum resource need not assume the collaborating parties are trustworthy, where the security of this process relies on the intrinsic nature of collective steering. Thus, it significantly reduces the device requirements in the network, and may provide unique conceptual tools for one-sided, device-independent QSS. In particular, a latest experiment implemented in optical system has observed multipartite EPR steering and genuine tripartite entanglement [3]. Here, we present a practical scheme for the demonstration of perfect one-sided device-independent QSS [4]. The scheme involves a three-mode optomechanical system in which a pair of independent cavity modes is driven by short laser pulses and interact with a movable mirror. We demonstrate that by tuning the laser frequency to the blue (anti-Stokes) sideband of the average frequency of the cavity modes, the modes become mutually coherent and then may collectively steer the mirror mode to a perfect EPR state. The scheme is shown to be experimentally feasible, it is robust against the frequency difference between the modes, mechanical thermal noise and damping, and coupling strengths of the cavity modes to the mirror.