Measuring qubit quasi-probability distributions behind out-of-time-ordered correlators*

The non-classicality of the quasi-probability distribution (QPD) behind an out-of-time-ordered correlator (OTOC) is a more nuanced witness for information scrambling than the OTOC itself. We use the method introduced in Phys. Rev. A 98, 012132 (2018) to provide different experimental protocols for obtaining such a QPD in a multi-qubit system. We show that by strategically averaging sequential measurements of any strength, we can reconstruct both OTOCs and QPDs in spite of disturbances caused by intermediate strong measurements.