Entanglement verification and steering when Alice and Bob cannot be trusted

Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of trust required, between the referee and each observer. Here it is shown that the need for any degree of trust of the observers by the referee can be completely removed via the referee using classical and quantum communication channels appropriately. In particular, trust-free verification of Bell nonlocality, Einstein-Podolsky-Rosen steering, and entanglement, respectively, requires two classical channels, one classical and one quantum channel, and two quantum channels. These channels correspond to suitable inputs of quantum randomness by the referee, which prevent the observers from mimicking entanglement using shared classical randomness. Our results generalize recent work by Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], and offer a perspective on the operational significance of that work. They also offer the possibility of simpler experimental demonstrations of the basic idea of quantum-refereed nonlocality tests.

Figure 1

Quantum-refereed games replace trust by quantum channels. Shaded regions indicate trust by the referee, Charlie, in the indicated party and in the quantum mechanical description of his or her apparatus. (Charlie's trust in himself is only indicated when he has a quantum state preparation device which he must trust.) Dashed lines represent classical channels and full lines represent quantum channels. The first column represents conventional nonlocality tests with classical channels, with trust in the appropriate parties as introduced in Refs. [7, 8]; the second column represents the corresponding quantum-refereed tests. Trust in Alice and/or Bob can thus be substituted by trust in Charlie's state preparation devices and quantum channels to the corresponding party, to demonstrate (a) entanglement and (b) EPR steering. Demonstration of (c) Bell nonlocality is unaltered as no party is assumed to be trusted.