## 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);