Not to be confused with DistPH, as in DistNP.
A middle-ground between classical and quantum proofs. Provers send (independent) probability distributions, or mixed states. After all proofs are sent, the verifier draws one sample from each proof.
If the proofs are allowed to be correlated, then the hierarchy collapses to just two levels as for QEPH.
Defined in [GY24] and shown to collapse to the standard definition of PH.
No class.