Physics – Quantum Physics
Scientific paper
2009-06-19
Physics
Quantum Physics
15 pages, 1 figure; added references, corrected typos; minor changes
Scientific paper
We introduce a point-line incidence geometry in which the commutation relations of the real Pauli group of multiple qubits are fully encoded. Its points are pairs of Pauli operators differing in sign and each line contains three pairwise commuting operators any of which is the product of the other two (up to sign). We study the properties of its Veldkamp space enabling us to identify subsets of operators which are distinguished from the geometric point of view. These are geometric hyperplanes and pairwise intersections thereof. Among the geometric hyperplanes one can find the set of self-dual operators with respect to the Wootters spin-flip operation well-known from studies concerning multiqubit entanglement measures. In the two- and three-qubit cases a class of hyperplanes gives rise to Mermin squares and other generalized quadrangles. In the three-qubit case the hyperplane with points corresponding to the 27 Wootters self-dual operators is just the underlying geometry of the E6(6) symmetric entropy formula describing black holes and strings in five dimensions.
Lévay Péter
Vrana Peter
No associations
LandOfFree
The Veldkamp space of multiple qubits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Veldkamp space of multiple qubits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Veldkamp space of multiple qubits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-401656