Need of Tangle calculation using code and Numerically

[Appu]

Homework Statement

How to find the tangle for the 3 qubit state in GHZ class and W class? (Using code in MATLAB and also numerically)

Relevant Equations

Tangle equation

= tangle equation

= Inequality condition

= partial trace formula.

To find the tangle, we need the square concurrence value of ABC states as mentioned in a tangle equation. I am not able to find the value of square concurrence.

 

[Nate810]

The tangle equation is given by:T=1/4 (C_A^2 + C_B^2 + C_C^2 - 2C_AC_B - 2C_BC_C - 2C_AC_C),where C_A, C_B and C_C are the concurrences between subsystems A, B and C respectively.To solve for the tangle, we need to first calculate the concurrence of each subsystem. This can be done using the partial trace formula, which is given by:C_AB = Tr[sqrt(ρAB*σAB*ρAB*σAB)] - Tr[ρAB²],where ρAB is the density matrix of the composite system AB and σAB is the swap operator. Similarly, the concurrences for subsystems B and C can be calculated using the same formula with appropriate substitutions. Once the concurrences for all three subsystems have been calculated, we can then plug them into the tangle equation to obtain the tangle.