Classification of multipartite entanglement

[munirah]

Good Morning.

I need some help according to how to classify the multipartite state.
from my reading, the classification according to Local Unitary (LU) and stochastic local operation and classical communication (SLOCC).

How the state can be classify from LU to SLOCC?

 

[Strilanc]

It's not clear what you're asking.

Two quantum states distributed amongst multiple parties are equivalent under SLOCC if the parties can transform one state into the other, and vice versa, with negligible error, using local quantum operations but only classical communication.

Of course it can get quite complicated. Sometimes the conversion is not 1:1, like you might need two copies of A to make one B. Sometimes the conversion is only one-way, where you can make Bs from As but can't make As from Bs. And apparently sometimes an A can't be turned into a B unless you have a quantum catalyst state C which will be used during, but ultimately end up unaffected by, the conversion operation.

 

[munirah]

It's not clear what you're asking.

Two quantum states distributed amongst multiple parties are equivalent under SLOCC if the parties can transform one state into the other, and vice versa, with negligible error, using local quantum operations but only classical communication.

Of course it can get quite complicated. Sometimes the conversion is not 1:1, like you might need two copies of A to make one B. Sometimes the conversion is only one-way, where you can make Bs from As but can't make As from Bs. And apparently sometimes an A can't be turned into a B unless you have a quantum catalyst state C which will be used during, but ultimately end up unaffected by, the conversion operation.

First of all thank you because respond to my question.

A.From your answered, what it means by
1.with negligible error
2. using local quantum operations but only classical communication.B.What I understand is, may you reconfirm me that what I understand is true or not?
1.LU is can be said subset to SLOCC. mean that SLOCC still used Unitary operator buat in positive probability.that mean some operation in LU cannot be done in SLOCC.
2. SLOCC used invertible local Operator (ILO) that transform A to B. ?
3. Both LU and SLOCC must monotone under local operations and classical communication (LOCC)?

C. Here , my question is,given a state,
|v>=1/2 ( |0>|w> + |1>U (tensor product) U |w>)
used LU with U is given in certain matrix.

Can I used SLOCC here to change LU to SLOCC?
And How it can be done?

thanks you