Ironically, of all the posts I scheduled to run while I was away on vacation last week, the only one which didn’t get automatically posted was the one saying that I’d be away and that the next weeks posts would be scheduled. Doh. So yeah, I was away.
For your viewing pleasure, Greek boats
and a Greek church
Bonus points for anyone who can identify this Greek town:
O brave new quantum world!
Did you drink Ouzo?
The name of the town is not Ouzo. 🙂
Navarone? 😛
While you were gone to the Dodecanese islands or wherever:
arXiv:0808.3849 (cross-list from quant-ph)
Title: Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
Authors: Peter Levay (BUTE), Metod Saniga (ASTRINSTSAV), Peter Vrana (BUTE)
Comments: 21 pages, 5 figures, 2 tables
Subjects: Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)
The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former set being in a bijective correspondence with the 7 points, 7 lines and 21 flags, whereas those of the latter set having their counterparts in 28 anti-flags of the plane. This representation naturally extends to the one in terms of the split Cayley hexagon of order two. 63 points of the hexagon split into 9 orbits of 7 points (operators) each under the action of an automorphism of order 7. 63 lines of the hexagon carry three points each and represent the triples of operators such that the product of any two gives, up to a sign, the third one. Since this hexagon admits a full embedding in a projective 5-space over GF(2), the 35 symmetric operators are also found to answer to the points of a Klein quadric in such space. The 28 antisymmetric matrices can be associated with the 28 vertices of the Coxeter graph, one of two distinguished subgraphs of the hexagon. The PSL_{2}(7) subgroup of the automorphism group of the hexagon is discussed in detail and the Coxeter sub-geometry is found to be intricately related to the E_7-symmetric black-hole entropy formula in string theory. It is also conjectured that the full geometry/symmetry of the hexagon should manifest itself in the corresponding black-hole solutions. Finally, an intriguing analogy with the case of Hopf sphere fibrations and a link with coding theory are briefly mentioned.
No one guessed it. It’s the main town on Andros, known as Andros town or Chora.
Thessaloniki?