4
$\begingroup$

We know the four Bell states are the maximal entangled states for two-qubit states, and we know if a state cannot be written as the tensor product by its subsets, then it is a entangled state, so is there a definition of maximal entangled state?

$\endgroup$
2
  • $\begingroup$ are you asking specifically about maximal entanglement for multipartite states? $\endgroup$
    – glS
    Sep 22 '21 at 14:13
  • $\begingroup$ Yes, some description about maximal entanglement for multipartite states. $\endgroup$
    – KarryMa
    Sep 22 '21 at 14:15
1
$\begingroup$

A pure state is said to be maximally entangled if the Von Neumann Entropy $S(\rho_{A})$, where $\rho_{A}=Tr_{B}(\rho_{AB})$ is the maximum value. ie $S(\rho_{A})=log(d)$ where $d$ is the dimension of the subsystem $A$

Edit: Just gonna add in here that, in the case of multipartite states, the entropy of the marginals in any bipartition of said state should be log(d), where $d$ in this case is the minimum over the dimensions of the systems involved in said bipartition.

$\endgroup$
4
  • $\begingroup$ What if three-qubit system (that is , multipartite system)? $\endgroup$
    – KarryMa
    Sep 22 '21 at 13:56
  • $\begingroup$ You don't necessarily need subsystem B to be a single subsystem. What I am taking here are biparitions. A tripartite state would be maximally entangled if, upon tracing out any of the other 2 subsystems, the entropy of the remaining state in the subsystem that is left is log(d) $\endgroup$ Sep 22 '21 at 13:59
  • 2
    $\begingroup$ you might want to specify that this applies to pure states. Otherwise, the bipartite state $I\otimes I/dd'$ (with $d,d'$ dimensions of two spaces) also has "maximal entropy". $\endgroup$
    – glS
    Sep 22 '21 at 14:15
  • $\begingroup$ This is a good catch. I guess I just assumed that was what they were referring to given the only mentioned state was the bell states. $\endgroup$ Sep 22 '21 at 14:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.