|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'503'724
Articles rated: 2609
23 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States | | Paul B. Slater
; Charles F. Dunkl
; | | Date: |
10 Nov 2014 | | Abstract: | In [1] and [2], a formula, incorporating a $5F4$ hypergeometric function, for
the Hilbert-Schmidt-averaged determinantal moments $<
|
ho^{PT}|^{n}|
ho|^{k}> /< |
ho|^{k}>$, for $4 imes 4$ density-matrices
($
ho$), was applied with $k=0$ to the generalized two-qubit
separability-probability question. We now observe that the formula can be
viewed more broadly, taking $k = K -N$, as yielding the "induced measures in
the space of mixed quantum states" of Zyczkowski and Sommers [3], where $N=4$
in the generalized two-qubit cases under consideration. The dimension, $K$, of
the ancilla/environment space, equals $N$ in the particular Hilbert-Schmidt
instance. As in the earlier work [1,2], a high-precision density-approximation
(inverse) procedure of Provost [4], incorporating the first 11,401 such
determinantal moments, strongly indicates that the induced-measure separability
probabilities ($k =1, 2,...$) assume interesting, relatively simple rational
values in the two-re[al]bit ($alpha = frac{1}{2}$), two-qubit ($alpha = 1$)
and (standard) two-quater[nionic]bit ($alpha =2$) cases. One striking example
is that for $k=3$, the $alpha =1$ separability probability is found to be
$frac{27}{38}= frac{3^3}{2 cdot 19}$ (to fifteen decimal places). In fact,
based on extensive calculations ($k =0,...,15,...$) of this nature, we are able
to deduce rather simple companion (rebit, qubit, quaterbit) formulas that
successfully reproduce the rational values assumed for general $k$. | | Source: | arXiv, 1411.2561 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER