Click here to edit contents of this page.
Click here to toggle editing of individual sections of the page (if possible). Watch headings for an "edit" link when available.
Append content without editing the whole page source.
Check out how this page has evolved in the past.
If you want to discuss contents of this page - this is the easiest way to do it.
View and manage file attachments for this page.
A few useful tools to manage this Site.
See pages that link to and include this page.
Change the name (also URL address, possibly the category) of the page.
View wiki source for this page without editing.
View/set parent page (used for creating breadcrumbs and structured layout).
Notify administrators if there is objectionable content in this page.
Something does not work as expected? Find out what you can do.
General Wikidot.com documentation and help section.
Wikidot.com Terms of Service - what you can, what you should not etc.
Wikidot.com Privacy Policy.
Reference [107] by Dür, Vidal and Cirac demonstrates that SLOCC operations are equivalent to invertible operations and preserves rank of a state, whereas LOCC operations can decrease rank (going from entangled to unentangled).
If
(1)is the Schmidt decomposition of the two-qubit state $\ket{\psi}$, then $\ket{\psi}$ is entangled when there are two terms and the Schmidt rank is 2, and it is unentangled when there is only one term and the Schmidt rank is 1.
Since SLOCC preserves rank, SLOCC operations have two orbits or equivalence classes on two-qubit states, the entangled states and the unentangled states.
From the perspective of invertible operations, an unentangled state in the Schmidt decomposition basis has vector either $(\lambda_0,0,0,0)$ or $(0,0,0,\lambda_1)$ and there is an invertible operation relating these:
(2)Likewise, two entangled states $(\lambda_0,0,0,\lambda_1)$ and $(\lambda_0',0,0,\lambda_1')$ can be linked by an invertible transformation:
(3)