Fig. 1: Pauli polytope for three fermions in six orbitals.
From: Open quantum system violates generalized Pauli constraints on quantum device
A convex set, known as the Pauli polytope, formed from the ordered natural occupations of the one-particle reduced density matrix (1-RDM) for three fermions in six orbitals. The sets of occupations lying inside the yellow region of the polytope, i.e., obeying the generalized Pauli constraints (GPCs), are compatible with at least one closed (pure-state) quantum system. Sets of natural occupations that lie in the blue region of the polytope, i.e., violating the GPCs, are only compatible with an open (ensemble) quantum system. The labeled points represent characteristic entangled states captured by the polytope, \(\left\vert W\right\rangle\) (\(\frac{1}{3}\),\(\frac{1}{3}\),\(\frac{1}{3}\)), \(\left\vert \,{{\mbox{EPR (Einstein-Podolsky-Rosen)}}}\,\right\rangle\) (\(\frac{1}{2}\),\(\frac{1}{2}\),0), and \(\left\vert \,{{\mbox{GHZ (Greenberger-Horne-Zeilinger)}}}\,\right\rangle\) (\(\frac{1}{2}\),\(\frac{1}{2}\),\(\frac{1}{2}\)), and an unentangled state \(\left\vert \,{{\mbox{Slater}}}\,\right\rangle\) (0,0,0) for this system.
