Mladen Pavicic
Hu and Center of Excellence CEMS, Institute Rudjer Boskovic, Croatia
Mladen Paivicic is a full professor at Photonics and Quantum Optics Research Unit of the Center of Excellence for Advanced Materials and Sensing Devices (CEMS) at the Institute Rudjer Boskovic, Zagreb, Croatia and a visiting professor at the Nanooptics Group at the Institute of Physics of the Humboldt-University of Berlin, Germany. One can find his biography, bibliography, and other details at the following web sites: https://www.irb.hr/users/mpavicic/http://cems.irb.hr/en/research-units/photonics-and-quantum-optics/There are also a number of videos on his lectures and talks athttp://youtube.com/quantumpavicic
As quantum contextuality proves to be a necessary resource for
universal quantum computation [1], we present a general method
for vector generation of Kochen-Specker (KS) contextual sets in
the form of hypergraphs. The method supersedes all three previous
methods: (i) fortuitous discoveries of smallest KS sets, e.g. [2],
(ii) exhaustive upward hypergraph-generation of sets, e.g., [3],
and (iii) random downward generations of sets from fortuitously
obtained big master sets, e.g., [4,5]. In contrast to all previous
works, we can generate a master set which contains (and thus can
exhaustively enumerate) all possible KS sets that can be assigned
starting with nothing but a few simple orthogonal vectors which we
can readily obtain on any PC. It is for the first time since the
first KS set, designed half a century ago, that a method of
generating arbitrary KS sets in arbitrary dimensional Hilbert
spaces from the simplest possible vector sets has been discovered. All KS sets obtained in the last half a century and all KS sets that exist readily follow from
that discovery.
Since quantum contextuality proves to be of increasing importance
in quantum computation and communication, it is important to
generate sufficiently large sets to enable varieties of different
implementations and to obtain their main features and information
on their structure. Our method of generating contextual set
provides just that.
In Fig. 1, we present the 4-dim 972-1852 KS class (972 vectors with
1852 orthogonalities) containing the previously obtained 60-105 class.
Both are determined by the same set of elementary vectors but the
60-105 method cannot "see" the whole 972-1852 class.
In Fig. 2, we present the 6-dim star/triangle class obtained
from the same vectors from which the smallest set 21-7 was obtained
[6,7]. All attempts to generate the class from the letter set via
standard methods in [6] failed.
MSE grants Nos. KK.01.1.1.01.0001 and 533-19-15-0022. Isabella, CRO-NGI, and Bura supports are acknowledged.
References:
[1] Howard, M. et al., Nature 510, 351 (2014);
[2] Cabello, A. and Garcia-Alcaine, G., Phys. Rev. Lett. 80, 1797 (1998).
[3] Pavicic, M., Merlet, J. P., McKay, B. D., and Megill, N. D., J. Phys., A 38, 1577 (2005);
[4] Pavicic, M., Phys. Rev. A 95, 062121 (2017);
[5] Waegell, M. and Aravind, P. K., Phys. Rev. A, 88, 012102 (2013);
[6] Lisonek, P. et al., Phys. Rev. A 89, 160501 (2014);
[7] Canas, G. et al., Phys. Rev. Lett. 111, 090404 (2014);
