Fault-tolerant distribution of GHZ states and controlled DSQC based on parity analyses.

Based on the circuit including linear optical elements, a fault-tolerant distribution of GHZ states against collective noise among three parties is proposed. Additionally, two controlled DSQC protocols using the shared GHZ states as quantum channels are also presented under the charge of the controller. The first controlled DSQC protocol applies single parity analysis based on weak cross-Kerr nonlinearities. The receiver Bob performs single-photon measurement to obtain the secret information after the outcome publication of the single parity analysis executed by the sender Alice. The second protocol applies dense coding to double information transmission capacity, and the double parity analyses based on weak cross-Kerr nonlinearities are performed to obtain the secret information.