Capacity of a Simultaneous Quantum Secure Direct Communication Scheme between the Central Party and Other M Parties

We analyse the capacity of a simultaneous quantum secure direct communication scheme between the central party and other M parties via M+1-particle GHZ states and swapping quantum entanglement. It is shown that the encoding scheme should be secret if other M parties wants to transmit M+1 bit classical messages to the centre party secretly. However, when the encoding scheme is announced publicly, we prove that the capacity of the scheme in transmitting the secret messages is 2 bits, no matter how large M is.