2003/06/19 by Paul B. Slater, Slater, Paul B.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0306132
eight pages, two tables, revtex4
arxiv created 2003/06/19 · openalex publication_date 2003/06/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous study (quant-ph/0207181), we formulated a conjecture that arbitrarily coupled qubits (describable by 4 x 4 density matrices) are separable with an a priori probability of 8/(11 π2) = 0.0736881. For this purpose, we employed the normalized volume element of the Bures (minimal monotone) metric as a probability distribution over the fifteen-dimensional convex set of 4 x 4 density matrices. Here, we provide further/independent (quasi-Monte Carlo numerical integration) evidence of a stronger nature (giving an estimate of 0.0736858 vs. 0.0737012 previously) for this conjecture. Additionally, employing a certain ansatz, we estimate the probabilities of separability based on certain other monotone metrics of interest. However, we find ourselves, at this point, unable to convincingly conjecture exact simple formulas for these new (smaller) probabilities.