Measuring Entanglement - Theory

 

• trace distance = 0 for no entanglement, 1 for max entanglement = 1-fidelity

   

• fidelity = (|<A,B>|/(||A||*||B||))²

  where A (B) is the reduced state with qubit k equal to 0 (1)

   

• If qubit k is not entangled with any of the other qubits,

  then the reduced state A should be the same as the reduced state B,

  i.e. the reduced state should be independent of qubit k.

   

• <A,B>/(||A||*||B||)) is the cosine of the angle between vectors A and B.

   

• A and B represent the same state if the angle is 0 or 180 degrees,

  which corresponds to the cosine having a magnitude squared value of 1.