# Can “experimental data from a quantum computer” be used to test separability probability conjectures?

An article entitled "Experimental data from a quantum computer verifies the generalize Pauli exclusion principle" by Scott E. Smart, David I. Schuster, and David A. Mazziotti has just appeared

In the study, they generate sets of random pure states of 3 fermions in 6 orbitals and examine their 1-RDM's (reduced density matrices). For this purpose, they employ "the IBM Quantum Experience devices (ibmqx4 and ibmqx2), available online, in particular, the 5-transmon quantum computing device". Can one adapt their approach to testing the "separability probability" question (arXiv:quant-ph/9804024) in any form (fermionic, or otherwise)?

In particular, can the conjectures that the two-qubit separability probabilities are $$\frac{8}{33}$$, $$\frac{25}{341}$$ or $$1-\frac{256}{27 \pi^2}$$, depending upon the choice of Hilbert-Schmidt, Bures or operator monotone function $$\sqrt{x}$$ measures (arXiv:1701.01973, arXiv:1901.09889) be evaluated? If one could generate random (using Fubini-Study measure) pure four-qubit states, and find the reduced two-qubit systems, then perhaps one could examine the Hilbert-Schmidt instance (p. 422 of Bengtsson-Zyczkowski monograph).

I see that there is 2011 and subsequent work of J. A. Miszczak (arXiv:1102.4598) concerning the (Mathematica) generation of random numbers through quantum processes, and their use in the production of random quantum states (such as I am seeking)--through standard (Ginibre-ensemble/random matrix theory) algorithms. But, I think, this is (presently?) comparatively slow in relation to pseudo-random means. Also, can the random states be generated "more directly" with the IBM devices? (Smart, Schuster, Mazziotti prepare initial pure states and then perform "arbitrary unitary transformations" ["generated on the quantum computer"] to obtain random pure states.)