Finite set of invariants to characterize local Clifford equivalence of   stabilizer states
  The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists a local Clifford operation which maps the first state to the second. We present a finite set of invariants which completely characterizes the LC equivalence class of any stabilizer state. Our invariants have simple descriptions within the binary framework in which stabilizer states are usually described. 
M. Van den Nest, J. Dehaene, B. De Moor