Relative volume of separable bipartite states
Rajeev Singh, Ravi Kunjwal, R. Simon · Physical Review A · 2014
Every choice of an orthonormal frame in the $d$-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, to the classical statistical state space of the system; the quantum state space itself can thus be profitably viewed as an $\text{SU}(d)$ orbit of classical state spaces, one for each orthonormal frame. We exploit this connection to study the relative volume of separable states of a bipartite quantum system. While the two-qubit case is studied in considerable analytic detail, for higher-dimensional systems we fall back on Monte Carlo. Several insights seem to emerge from our study.