Conditional Mutual Information of Bipartite Unitaries and Scrambling

Understand

One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI).

• We study this quantity from a quantum information-theoretic perspective to clarify its role in diagnosing scrambling.
• When the CMI is zero, we find that the channel has a special normal form consisting of local channels between individual inputs and outputs.
• However, we find that arbitrarily low CMI does not imply arbitrary proximity to a channel of this form, although it does imply a type of approximate recoverability of one of the inputs.