A sufficient and necessary condition for 2n− 1 orthogonal states to be locally distinguishable in aC2⊗Cnsystem
Wei Jiang, Xi-Jun Ren, Yu-Chun Wu, Zheng-Wei Zhou, Guang‐Can Guo, Heng Fan · Journal of Physics A Mathematical and Theoretical · 2010
We investigate the local distinguishability of a set of orthogonal states on C2⊗Cn by mathematical induction. We prove that a set of 2n − 1 orthogonal states on C2⊗Cn can be locally discriminated by local operation and classical communication if and only if at most one of them is entangled, that is, the sum of Schmidt rank of these states should be no greater than the total Hilbert space dimension, 2n. Furthermore, we give some discussion about locally distinguishing any number of orthogonal states on C2⊗Cn and explain why this Schmidt-rank criterion cannot be generalized to locally discriminate any number of orthogonal states.