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24 January 2021
  » arxiv » quant-ph/0306132

 Article overview

Metric-dependent probabilities that two qubits are separable
Paul B. Slater ;
Date 19 Jun 2003
Subject quant-ph
AffiliationUniversity of California
AbstractIn 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 pi^2) = 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.
Source arXiv, quant-ph/0306132
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