Petr Pracna

PROJECTIVE RING LINE ENCOMPASSING TWO-QUBITS

We find that the projective line over the (noncommutative) ring of 2×2 matrices with coefficients in GF(2) fully accommodates the algebra of 15 operators (generalized Pauli matrices) characterizing two-qubit systems. The relevant subconfiguration consists of 15 points, each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the line. The operators can be identified one-to-one with the points such that their commutation relations are exactly reproduced by the underlying geometry of the points with the ring geometric notions of neighbor and distant corresponding to the respective operational notions of commuting and noncommuting. This remarkable configuration can be viewed in two principally different ways accounting for the basic corresponding 9+6 and 10+5 factorizations of the algebra of observables: first, as a disjoint union of the projective line over GF(2) × GF(2) (the “Mermin” part) and two lines over GF(4) passing through the two selected points that are omitted; second, as the generalized quadrangle of order two with its ovoids and/or spreads corresponding to (maximum) sets of five mutually noncommuting operators and/or groups of five maximally commuting subsets of three operators each. These findings open unexpected possibilities for an algebro-geometric modeling of finite-dimensional quantum systems and completely new prospects for their numerous applications.

Simultaneous Rovibrational Analysis of the ν2, ν3, ν5, and ν6 Bands of H312CF

Abstract A total of 4892 transition wavenumbers of the ν 2 , ν 3 , ν 5 , and ν 6 fundamental bands of H 3 12 CF and 1469 frequencies of the rotational transitions in the v 2 = 1, v 3 = 1, v 5 = 1, and v 6 = 1 vibrational states have been fitted simultaneously by taking explicitly into account various Coriolis interactions, l -type interactions, and α-resonance terms between and within the vibrational states. The standard deviation of the fit using 71 parameters was 8.10 × 10 −5 cm −1 for the infrared data and 0.198 MHz for the rotational data. This study clearly shows that in order to obtain a really quantitative fit of the highly precise data of vibration–rotational and rotational spectroscopy, it is necessary to fit all the data simultaneously using a variational approach. The deperturbed values of the upper state rotational constants differ significantly from those obtained previously in fitting the ν 3 and ν 6 bands as isolated bands and the ν 2 /ν 5 bands by a variational approach. This is important for the precise determination of the equilibrium structure of methyl fluoride (J. Demaison, J. Breidung, W. Thiel, and D. Papousek, Struct. Chem., in press). Besides this, the results can be used in further studies of the reduced Hamiltonians for more complicated systems of interacting vibrational levels.

From Cayley-Dickson Algebras to Combinatorial Grassmannians

Given a

Interactions in symmetric top molecules between vibrational polyads: rotational and rovibrational spectroscopy of low-lying states of propyne, H3C–C≡CH

2^N

Charting the real four-qubit Pauli group via ovoids of a hyperbolic quadric of PG(7, 2)

-dimensional Cayley-Dickson algebra, where

Rotational and rovibrational spectroscopy of CH3NC of the ground and ν4 = 1 vibrational states.

3 \leq N \leq 6

First analysis of the high resolution FTIR spectrum of the ν2 band of the FCO2 radical at 970.2 cm−1

, we first observe that the multiplication table of its imaginary units

Assignment of coherent anti-stokes Raman spectra of the ν1 bands of ammonia: 14ND3 and 15ND3

e_a

'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon

,

Rotational and rovibrational spectroscopy of the v 8 = 1 and 2 vibrational states of CH3NC

1 \leq a \leq 2^N -1