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Quasirandom estimations of two-qubit operator-monotone-based separability probabilities
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
Abstract
- We conduct a pair of quasirandom estimations of the separability probabilities with respect to ten measures on the 15-dimensional convex set of two-qubit states, using its Euler-angle parameterization. The measures include the (non-monotone) Hilbert-Schmidt one, plus nine others based on operator monotone functions. Our results are supportive of previous assertions that the Hilbert-Schmidt and Bures (minimal monotone) separability probabilities are $\frac{8}{33} \approx 0.242424$ and $\frac{25}{341} \approx 0.0733138$, respectively, as well as suggestive of the Wigner-Yanase counterpart being $\frac{1}{20}$. However, one result appears inconsistent (much too small) with an earlier claim of ours that the separability probability associated with the operator monotone (geometric-mean) function $\sqrt{x}$ is $1-\frac{256}{27 \pi ^2} \approx 0.0393251$. But a seeming explanation for this disparity is that the volume of states for the $\sqrt{x}$-based measure is infinite. So, the validity of the earlier conjecture--as well as an alternative one, $\frac{1}{9} \left(593-60 \pi ^2\right) \approx 0.0915262$, we now introduce--can not be examined through the numerical approach adopted, at least perhaps not without some truncation procedure for extreme values.<br />Comment: 19 pages, 16 figures--text moderately expanded, but sample size in main analyses doubled in size. To appear in International Journal of Quantum Information
- Subjects :
- Discrete mathematics
Quantum Physics
81P16, 81P40, 81P45, 60B20, 15B52
Physics and Astronomy (miscellaneous)
Operator (physics)
Convex set
FOS: Physical sciences
Quantum entanglement
Mathematical Physics (math-ph)
16. Peace & justice
01 natural sciences
010305 fluids & plasmas
Euler angles
symbols.namesake
Monotone polygon
Qubit
0103 physical sciences
symbols
Quantum information
Geometric mean
010306 general physics
Quantum Physics (quant-ph)
Mathematical Physics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....8c8178278a27091099d1f88209ab5e6a
- Full Text :
- https://doi.org/10.48550/arxiv.1910.07937