# How to calculate Quantum Discord for two qubit system using Qutip?

Quantum discord of a bipartite system can be determined as:

$${D_A}({\rho _{AB}}) = I({\rho _{AB}}) - {J_A}({\rho _{AB}}),$$ The subscript of $$A$$ denotes that the measurement has been performed on the subsystem $$A$$. The mutual information is defined as - $$I({\rho _{AB}}) = S({\rho _A}) + S({\rho _B}) - S({\rho _{AB}}),$$

the classical correlation is defined as -

$${J_A}({\rho _{AB}}) = S({\rho _A}) - \mathop {\min }\limits_{\{ \Pi _I^A\} } \sum\limits_i {{p_i}S({\rho _{\left. B \right|i}})} ,$$ $$S({\rho _{\left. B \right|i}}) = {1 \over {{p_i}}}t{r_A}\left( {\Pi _i^A \otimes {I_B}} \right){\rho _{AB}}\left( {\Pi _i^A \otimes {I_B}} \right)$$

How does one calculate this quantity, computationally say, using Qutip or any other package/software, is there a code developed for this? Can anyone suggest an algorithm? Doing this analytically for any arbitrary density matrix, $$\rho_{AB}$$ is not feasible.

• related github issue: github.com/qutip/qutip/issues/1450
– poig
Jun 30, 2022 at 12:41
• Yes, but the thread provides no solution, and possibly no progress has happened since that conversation. I was hoping to find someone who might have done the computation and would have some advice. Jun 30, 2022 at 12:46