Mads, Thanks for emphasizing the fact that when arg1 is already a quantum state, the second arg2 is there to transform the state to a new basis. However, my question was really the following: Since "Bell" and "PhiPlus" are the same state, why should any result involving a call to QuantumState[] (regardless of the basis specification) be different? In other words, each of the two rows in my table should be identical, since the only difference between them is arg1 (i.e., either "Bell" or "PhiPlus").

Michael, the 2nd argument of QuantumState[arg1,arg2] has the information of QuantumBasis When arg1 is already a quantum state, the meaning of QuantumState[QuantumState[...],arg2] is to transform QuantumState[...] into new basis arg2 Of course, new basis should match the dimensionality of original state QuantumState[...]