dorsal/arxiv
View SchemaMetric-dependent probabilities that two qubits are separable
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306132 |
| URL | https://arxiv.org/abs/quant-ph/0306132 |
Abstract
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 \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.
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"abstract": "In a previous study (quant-ph/0207181), we formulated a conjecture that\narbitrarily coupled qubits (describable by 4 x 4 density matrices) are\nseparable with an a priori probability of 8/(11 \\pi^2) = 0.0736881. For this\npurpose, we employed the normalized volume element of the Bures (minimal\nmonotone) metric as a probability distribution over the fifteen-dimensional\nconvex set of 4 x 4 density matrices. Here, we provide further/independent\n(quasi-Monte Carlo numerical integration) evidence of a stronger nature (giving\nan estimate of 0.0736858 vs. 0.0737012 previously) for this conjecture.\nAdditionally, employing a certain ansatz, we estimate the probabilities of\nseparability based on certain other monotone metrics of interest. However, we\nfind ourselves, at this point, unable to convincingly conjecture exact simple\nformulas for these new (smaller) probabilities.",
"arxiv_id": "quant-ph/0306132",
"authors": [
"Paul B. Slater"
],
"categories": [
"quant-ph"
],
"title": "Metric-dependent probabilities that two qubits are separable",
"url": "https://arxiv.org/abs/quant-ph/0306132"
},
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