Timeline for Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities
Current License: CC BY-SA 4.0
25 events
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| Oct 30, 2020 at 17:14 | answer | added | Paul B. Slater | timeline score: 3 | |
| Oct 30, 2020 at 14:35 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
Duplicate > sign deleted
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| Oct 29, 2020 at 16:24 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
1 > v constraint also added to 5D integration statement, for purposes of further analyses
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| Oct 29, 2020 at 15:52 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
The constraint 1 - v - w - x - y - z > 0 has been added to the 5D integration Boole command, as further analysis indicates is required
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| Oct 3, 2020 at 12:56 | comment | added | Paul B. Slater | Apparently, the "price-to-pay" for the more concise (LeafCount 48) formula of JimB above as opposed to the 2009 (LeafCount 77) formula is that the argument (18/Sqrt[50 + 17 Sqrt[2]]) of the single inverse trigonometric function is much more "idiosyncratic" in nature than the multiple $\sqrt{2}$' arguments in the 2009 case. Though the two formulas are undoubtedly equivalent--as numerics indicate--the FullSimplify command apparently does not reveal that. It seems that some transformations would be needed to show their equivalence. | |
| Oct 3, 2020 at 3:21 | comment | added | Paul B. Slater | Agrees to high numerical precision with the (less concise) 2009 formula of Slater presented in the statement of the question. Also, strikingly, it has the same four-term structure as the (complex) two-qubit counterpart 29902415923/497664 - 50274109/(512 Sqrt[2]) - (3072529845 [Pi])/( 32768 Sqrt[2]) + (1024176615 ArcCos[1/3])/(4096 Sqrt[2]) derived by JimB in his answer to mathematica.stackexchange.com/questions/230127/… These two derivations were obtained within the Tessore unconstrained framework--not yet available in 2009. | |
| Oct 2, 2020 at 21:01 | comment | added | JimB |
Using the same approach as in mathematica.stackexchange.com/questions/230127/…, I get 327574875999612773528659/95105071448064 - 2951081236201839/(524288 Sqrt[2]) - (15390446918294583135 \[Pi])/(17179869184 Sqrt[2]) + (15390446918294583135 ArcCsc[18/Sqrt[50 + 17 Sqrt[2]]])/(2147483648 Sqrt[2]) for the 3D integral.
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| Sep 28, 2020 at 0:48 | history | edited | AsukaMinato | CC BY-SA 4.0 |
refine the formula
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| Sep 28, 2020 at 0:28 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
Procedures of JimB for dealing with the unconstrained integral inserted
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| Sep 28, 2020 at 0:05 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
Equivalent unconstrained 3D integration problem now given.
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| Sep 27, 2020 at 20:28 | history | edited | Paul B. Slater | CC BY-SA 4.0 |
title expansion
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| Sep 27, 2020 at 20:14 | history | asked | Paul B. Slater | CC BY-SA 4.0 |