Quantum Contextuality

Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, in our paper in “Quantum” (Impact Factor 6.4) Mladen Pavičić, “Quantum Contextuality,” Quantum 7, 953 (2023); DOI 10.22331 q-2023-03-17-953 we focus on engineering the sets that support those resources and on determining their structures and properties. Such engineering and subsequent implementation rely on discrimination between statistics of measurement data of quantum states and those of their classical counterparts. Their discriminators are hypergraphs which determines how states supporting a computation or communication are arranged.

It turns out that contextual quantum non-binary hypergraphs, in contrast to classical binary ones, are essential for designing quantum computation and communication and that their structure and implementation rely on such non-binary vs. binary differentiation. We are able to generate arbitrarily many contextual sets from simplest possible vector components and then make use of their structure by implementing the hypergraphs with the help of YES-NO measurements so as to collect data from each gate/edge and then postselect them. At the same time this procedure shows us that we have to carry out measurements on complete set of states before we postselect them. As an example the Klyachko pentagon cannot lie in a plane, as shown in the figure; only its postselected states do.

Klyachko’s pentagon

Other considered discriminators are six hypergraph inequalities. They follow from two kinds of statistics of data. One kind of statistics, often applied in the literature, turn out to be inappropriate and consequently two kinds of inequalities turn out not to be noncontextuality inequalities. Results are obtained by making use of universal automated algorithms which generate hypergraphs with both odd and even numbers of hyperedges in any odd and even dimensional space – in this paper, from the smallest contextual set with just three hyperedges and three vertices to arbitrarily many contextual sets in up to 8-dimensional spaces. Higher dimensions are computationally demanding although feasible.

First demonstration of quantum communication among three states

5 August 2021   Encrypted audio-video communication has been established between Italy, Slovenia and Croatia with the help of quantum technology!

The first public demonstration of quantum communication between three countries: Italy, Slovenia and Croatia, was demonstrated today as a part of the G20 meeting in Trieste. It was established among Trieste, Ljubljana and Rijeka. Thanks to scientists and experts led by the Ruđer Bošković Institute (RBI) within the Croatian Quantum Communication Infrastructure Consortium (CroQCI), Croatia, although not a member of the G20, found itself alongside the richest and most influential countries.

Dr. Mario Stipčević and Dr. Martin Lončarić

The demonstration was organized by Prof. Angelo Bassi from the Department of Physics of the University of Trieste and the Quantum Communications Group of the National Institute of Optics (CNR-INO) led by Dr. Alessandro Zavatta.

In Slovenia, the demonstration was led by Prof. Rainer Kaltenbaek and Prof. Anton Ramšak from the Faculty of Mathematics and Physics, University of Ljubljana, with the technical support of Telekom Slovenije, while in Croatia this endeavour was led by Dr. Mario Stipčević and Dr. Martin Lončarić from the Ruđer Bošković Institute with the support of colleagues from the Faculty of Transport and Traffic Sciences in Zagreb and the telecom company OIV – Digital Signals and Networks.

“The Croatian side, in addition to full quantum communication on the 100.5-kilometer-long Trieste-Rijeka route, here for the first time in the world publicly demonstrated the so-called “quantum-enhanced cryptography”, through which Rijeka is connected to Zagreb. The device that made this possible is the result of cooperation between the “PCE” Marine Electronic Center from Split and the Ruđer Bošković Institute from Zagreb. It is an intermediate step that offers security less than quantum cryptography (which is absolute), but also significantly higher than conventional crypto solutions, and at a significantly lower cost than quantum cryptography.” explained Dr. Mario Stipčević, head of the Laboratory for Photonics and Quantum Optics at the RBI and one of the coordinators of the demonstration in Croatia.

“With the successful realization of this endeavour, our scientists and experts broke the ice and paved the way for the realization of quantum infrastructure in the Republic of Croatia. This proves Croatia’s readiness to participate in the construction of a pan-European quantum communication network”, said Dr. Stipčević.

Quantum communication satisfies the need for secure communication, which is a priority of all governments around the world. This technology achieves absolute security thanks to quantum encryption that works through photon exchange, which allows instantaneous detection of hacker intrusion attempts.

“The importance of today’s demonstration is further emphasized in the context of the future European Quantum Communication Infrastructure (EuroQCI) promoted by all EU member states and the European Commission with the support of the European Space Agency. From the very beginning, Croatia has been involved in shaping EuroQCI”, explains Dr. Martin Lončarić from the RBI, who, along with Dr. Stipčević, is the coordinator of these activities in Croatia.

“Today we have laid the foundation stone for a new European quantum infrastructure,” explained Tommaso Calarco, President of the European Quantum Community Network (QCN), “with unprecedented security, which by nature belongs to us”, he concluded.

The demonstration began with official greetings from representatives of the institutions, followed by a real musical treat prepared by three music quartets. Namely, the musicians, using the quantum cryptography established to demonstrate this communication, performed specially prepared musical works in each of the three countries.

The musical performance was achieved thanks to the cooperation of the Trieste Conservatory “Giuseppe Tartini” together with the Music Academies in Ljubljana and Zagreb.

The quartet of saxophonists of the Music Academy in Ljubljana (Miha Rogina soprano, saxophone, Nika Deželak alto saxophone, Agata Živoder tenor saxophone, Domen Koren baritone) performed “Tango virtuoso” by Thierry Escaich.

The String Quartet of the Academy of Music, University of Zagreb (Matej Žerovnik and Luka Kojundžić violin, Filip Kojundžić viola, Lucija Mušac cello) performed Fran Lhotka’s “Scherzo”, while the quartet of saxophonist of the Trieste Conservatory “Giuseppe Tartini” (soprano-saxophone Elia Sor Emma Marcolin, tenor saxophone Matilda Travain, baritone saxophone Marin Komadina), performed “Suite Hellenique” by Pedro Iturralde.

The implementation was supported by the Ministry of Foreign and European Affairs, the Ministry of Science and Education, the Ministry of the Sea, Transport and Infrastructure, the Ministry of Defense and the Agency Alan, as well as projects of the Croatian Science Foundation no. IPS-2020-01-2616 and MZO no. KK.

Additional information can be found here.

G20 video URL: https://youtu.be/LLc_YP7FngI

A trusted node-free eight-user metropolitan quantum communication network, Science Advances, 2 September 2020

Kvantni fizičari CEMS Fotonike s Instituta Ruđer Bošković (IRB) dio su međunarodnog tima znanstvenika koji je otkrio i eksperimentalno realizirao kvantnu komunikacijsku mrežu s više korisnika koju je nemoguće špijunirati. Ovo otkriće veliki  je korak prema potpuno sigurnoj i zaštićenoj mrežnoj komunikaciji. Rezultati ovog značajnog znanstvenog otkrića objavljeni su u prestižnom znanstvenom časopisu Science Advances.

Umjetnički doživljaj kvantne mreže (Anta Bučević, vizualni dizajner).

Participation on Humboldt-Kolleg conferention in Zagreb

PhD student Matej Peranić and physics student Mateja Batelić have participated on Humboldt-Kolleg conferention “Science and educational challenges facing Europe in the next decade” that was held in Zagreb on 10th and 11th October. They presented their work by posters titled Experimental generation of quantum entanglement and testing fundamentals of quantum physics and Improved circuits for a biologically-inspired random pulse computer. Their experimental work was done in Photonics and Quantum Optics Research Unit of Center of Excellence for Advanced Materials and Sensors.

Participation on 7th International Symposium on Optics & its applications (OPTICS-2019) and first prize for best student oral presentation

Member of Photonics and Quantum Optics Research Unit of Center of Excellence for Advanced Materials and Sensors, PhD student Matej Peranić participated on the 7th International Symposium on Optics & its applications (OPTICS-2019) that was held from 20.-24. September in Yerevan, Armenia. He was awarded with the first prize for best student oral presentation with the title The source of polarization entangled pairs of photons and testing Bell’s inequality.

Automated generation of Kochen-Specker sets

Quantum contextuality arguably plays an important role in the field of quantum communication and quantum computation, and in our paper in Scientific Reports (Nature journal; IF 4.122) Mladen Pavičić, Mordecai Waegell, Norman D. Megill and P.K. Aravind, “Automated generation of Kochen-Specker sets,” Scientific Reports,” 9, 6765 (2019) we focus on automated vector-component generation of the most explored and used contextual configurations—the so-called Kochen-Specker (KS) sets. They are represented by hypergraphs whose very structure delimit quantum contextuality from classical noncontextuality. When they can be assigned definite predetermined values, e.g., 0 and 1, as in classical computation, they are noncontextual, and when they cannot be assigned predetermined values, as in quantum computation, they are contextual and possess the KS property and become KS sets.

Since quantum contextuality turns out to be a necessary resource for universal quantum computation it becomes important to generate contextual sets of arbitrary structure and complexity to enable a variety of implementations. Up to now, two approaches have been used for massive generation of non-isomorphic KS sets: exhaustive generation up to a given size and downward generation from big master sets. The former faces low computational limits due to the exponential complexity of hypergraph generation and of finding their coordinatization. On the other hand, the latter masters were obtained together with their coordinatization but from serendipitous or intuitive connections with polytopes or Pauli operators or already known masters in lower dimensions. These masters, which we explored in our previous paper Pavičić, M., Physical Review A, 95, 06212 (2017), therefore provide us with a random choice of KS sets and their coordinatization. But what we need for implementations and applications is a method of finding KS sets for a coordinatization of our choice.

In order to find a solution to this problem we turned it upside-down. Instead of searching for vectors we might assign to chosen masters, we generate masters from basic vector components via automated sweeping through simplest of them, starting, e.g., from {-1,0,1} or {-i,0,i}. Next, we elaborate on features, algorithms, and methods which not only speed up the search for KS sets almost exponentially, but also enable arbitrary exhaustive generation of KS sets and their classes.

In the figure below we can see how much more superior our new method is, with respect to the previous ones, e.g. (a), where a master hypergraph with 60 vertices and 105 edges was obtained via Pauli operators. When we use the same vector components as in (a) we get a huge master hypergraph with 688 vertices and 1305 edges which contais a 432-1177 KS master hypergraph and sixteen 16-8 non-KS hypergraphs as shown in (f). Even when we drop the 5th component (+2), we still get a bigger KS master hypergraph (c) then the original (a).








Quantum entanglement of photons and Bell theorem test at CEMS

Photonics and Quantum Optics Research Unit of Center of Excellence for Advanced Materials and Sensors at the Ruđer Bošković Institute announces realization and measurement of quantum entanglement of photon pairs. The experimental setup is schematically shown in the figure. A 405 nm wavelength purple laser beam is fed into Sagnac interferometer containing a periodically-poled crystal of potassium titanil-phosphate (PPKTP), schematically shown below on the left. The actual setup is shown on the right. Thanks to the nonlinear optical nature of the crystal and the specifically selected orientation of its lattice axes, some of the purple photons undergo a process of spontaneous parametric downconversion and thus split into a pair of infrared photons that are quantum entangled in polarization. Quantum entanglement of photons was evaluated in two ways.


First, we measured correlation of polarization of paired photons. To that end, each photon is sent to one of the polarization-measuring stations, named Alice and Bob. The actual setup is shown below. Alice and Bob are each realized as a polarizer mounted on computer-controlled, motorized mount, followed by an optical-fiber-coupled photon detector, as shown in the photo of the actual setup.

Alice can measure polarization along one of 4 special orientations (horizontal (H), vertical (V), diagonal (D) and anti-diagonal (A)). For each of the Alice’s orientations, Bob rotates his polarization analyzer for a full circle and they evaluate probability of measuring a photon polarization along their respective orientation, as a function of Bob’s analyzer angle. The probability forms a sinusoidal fringe, as shown in the figure below. Visibility greater than 50% for all 4 fringes is not possible if photons in a pair have predetermined polarizations. On the other hand, if photons are entangled, then visibility of all 4 fringes can reach the theoretical maximum of 100%. With our source we have obtained: V= (99,8 +/- 0,6) %, V= (99,7 +/- 0,4) %, V= (98,5 +/- 0,4) %, V= (98,3 +/- 0,4) %, as shown in the figure, which indicates near-maximal entanglement of photons.

We also used the Bell’s theorem and performed measurement of Clauser, Horne, Shimony, Holt (CHSH) parameter S, to test the CHSH form of Bell’s inequality. Classical physics predicts S ≤ 2, while quantum physics allows 2 < S ≤ 2√2  2.828. We have experimentally obtained the value of S = 2,803 +/- 0,007 which is more than 114 standard deviations greater than the maximum value of 2 allowed by classical physics, again indicating the near-maximal entanglement.

These results demonstrate the non-local behaviour of quantum-entangled photon pairs, which is that the measurement of polarization performed on one photon has an immediate impact on the result of measurement of polarization on the other photon.