Related papers: Exact entanglement bases and general bound entangl…
This paper has been withdrawn by the authors, due to the discovery of paper 0201028 which predates it and contains most of it's results.
This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,
In quantum mechanics and quantum information, to establish the orthogonal bases is a useful means. The existence of unextendible product bases impels us to study the `entanglement bases' problems. In this paper, the concepts of entanglement…
This paper has been withdrawn by the author due to an error in the proof of Theorem 1.
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.
We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper
The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
This paper has been withdrawn by the author due to a crucial sign error in equation 1
This paper has been withdrawn due to a crucial error in the proof of the main theorem
This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.
There is an error in the proof of Theorem 1.1 that invalidates proofs of other theorems. Theorem 1.5 is unaffected.
The paper has been withdrawn by the author due to crucial error in formula (14) which does not satisfy conditions for S(x,y) domain if only d>2.
This paper has been withdrawn by the authors because M. Aschenbrenner pointed out that the proof of theorem 3.1 was incorrect.
This paper has been withdrawn by the author due to a crucial error in equation (51).
This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]
This paper has been withdrawn by the author due to a crucial sign error in equation 1.
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
This paper has been withdrawn by the authors due to an error.
This paper has been withdrawn by the author, due to an error in Proposition 2.2.