ar X iv : 1 30 4 . 01 28 v 1 [ qu an t - ph ] 3 0 M ar 2 01 3 Factoring 51 and 85 with 8 qubits

ar X iv : 0 90 1 . 19 68 v 3 [ qu an t - ph ] 2 9 Ju l 2 01 1 1 All the stabilizer codes of distance 3

We give necessary and sufficient conditions for the existence of stabilizer codes [[n, k, 3]] of distance 3 for qubits: n−k ≥ ⌈log2(3n+1)⌉+ǫn where ǫn = 1 if n = 8 4 m −1 3 +{±1, 2} or n = 4 m+2 −1 3 − {1, 2, 3} for some integer m ≥ 1 and ǫn = 0 otherwise. Or equivalently, a code [[n, n−r, 3]] exists if and only if n ≤ (4r − 1)/3, (4r − 1)/3 − n / ∈ {1, 2, 3} for even r and n ≤ 8(4 − 1)/3, 8(4 ...

ar X iv : m at h - ph / 0 10 30 34 v 1 2 5 M ar 2 00 1 MZ - TH 01 - 09 LPT - ORSAY 01 - 28 MULTIPLE NONCOMMUTATIVE TORI

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.

ar X iv : 1 11 1 . 37 97 v 1 [ qu an t - ph ] 1 6 N ov 2 01 1 Prony ’ s method and the connected – moments expansion

ar X iv : 0 71 0 . 34 25 v 2 [ qu an t - ph ] 1 4 N ov 2 00 7 Properties of the residual entanglement for n - qubits 1

X iv :0 71 0. 34 25 v2 [ qu an tph ] 1 4 N ov 2 00 7 Properties of the residual entanglement for n-qubits Dafa Li, Xiangrong Li, Hongtao Huang, Xinxin Li a Dept of mathematical sciences, Tsinghua University, Beijing 100084 CHINA b Department of Mathematics, University of California, Irvine, CA 92697-3875, USA c Electrical Engineering and Computer Science Department University of Michigan, Ann A...

ar X iv : 1 01 1 . 52 06 v 2 [ qu an t - ph ] 8 D ec 2 01 0 More non - locality with less entanglement

We provide an explicit example of a Bell inequality with 3 settings and 2 outcomes per site for which the largest violation is not obtained by the maximally entangled state, even if its dimension is allowed to be arbitrarily large. This complements recent results by Junge and Palazuelos (arXiv:1007.3042) who show, employing tools from operator space theory, that such inequalities do exist. Our ...