Counterfactual Bell-State Analysis

The Bell-state analysis to distinguish between the four maximally entangled Bell states requires the joint measurement on entangled particles. However, spatially separated parties cannot perform the joint measurement. In this paper, we present a counterfactual Bell-state analysis based on the chained quantum Zeno effect. This counterfactual analysis not only enables us to perform a complete Bell-state analysis, but also enables spatially separated parties to distinguish between the four Bell states without transmitting any physical particle over the channel.