  A sequence of moments encode the corresponding probability distribution.
Probing if quantum joint probability distribution can be retrieved from the
associated set of moments -- realized in the sequential measurement of a
dichotomic observable at different time intervals -- reveals a negative answer
i.e., the joint probabilities of sequential measurements do not agree with the
ones obtained by inverting the moments. This is indeed a reflection of the
non-existence of a bonafide grand joint probability distribution, consistent
with all the physical marginal probability distributions. Here we explicitly
demonstrate that given the set of moments, it is not possible to retrieve the
three-time quantum joint probability distribution resulting from quantum
sequential measurement of a single qubit dichotomic observable at three
different times. Experimental results using a nuclear magnetic resonance (NMR)
system are reported here to corroborate these theoretical observations viz.,
the incompatibility of the three-time joint probabilties with those extracted
from the moment sequence.

Quantum Physics