Fault tolerant controlled quantum dialogue against collective noise

Quantum system is inevitably affected by the external environment in the real world.Two controlled quantum dialogue protocols are put forward based on logicalχ-type states under collective noise environment.One is against collectivedephasing noise,while the other is against collective-rotation noise.Compared with existing protocols,there exist several outstanding advantages in our proposed protocols:Firstly,theχ-type state is utilized as quantum channels,it possesses better entanglement properties than GHZ state,W state as well as cluster state,which make it difficult to be destroyed by local operations.Secondly,two kinds of logicalχ-type states are constructed by us in theory,which can be perfectly immune to the effects of collective noise.Thirdly,the controller can be offline after quantum distribution and permission announcement,without waiting for all the participants to complete the information coding.Fourthly,the security analysis illuminates that our protocols can not only be free from the information leakage,but also resist against the interceptand-resend attack,the entanglement-and-measure attack,the modification attack,the conspiring attack,and especially the dishonest controller’s attacks.