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A priori probability that a qubitqutrit pair is separable  Paul B. Slater
;  Date: 
25 Nov 2002  Journal:  Journal of Optics B: Quantum and Semiclassical Optics, volume 5, issue 6, pages S651S656 (2003)  Subject:  quantph  Affiliation:  University of California  Abstract:  We extend to arbitrarily coupled pairs of qubits (twostate quantum systems) and qutrits (threestate quantum systems) our earlier study (quantph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis  again on the basis of numerical (quasiMonte Carlo) integration results, but now in a still higherdimensional space (35d vs. 15d)  we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubitqubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubitqutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubitqubitqubit and qutritqutrit cases.  Source:  arXiv, quantph/0211150  Services:  Forum  Review  PDF  Favorites 


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