2002/11/30 by Paul B. Slater
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1088/1464-4266/5/6/018
published as Journal of Optics B: Quantum and Semiclassical Optics, volume 5, issue 6, pages S651-S656 (2003) · 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjectures
arxiv created 2003/04/18 · openalex publication_date 2003/10/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (Slater 2002 Quantum Inf. Process. 1 387), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis—again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35D versus 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, , 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, , in the qubit–qubit 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 qubit–qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit–qubit–qubit and qutrit–qutrit cases.