Paper on “Non-Kochen-Specker Contexuality” has been selected as the cover paper of Entropy

Invited paper “Non-Kochen–Specker Contextuality” by Mladen Pavičić, Entropy, 25(8), 1117 (2023), DOI: 10.3390/e25081117, has been selected as the cover paper of issue 8 of Entropy Volume 25 (2023) and the publication charges were waived.

The cover story reads as follows.

Let us consider a triangular hypergraph with three vertices and three hyperedges, each pairwise connecting two of the vertices. If we tried to assign 0 and 1 to vertices, so that just one vertex within each of the three hyperedges is assigned 1 (condition X), we would realize that this is not possible. The hypergraph exhibits a non-Kochen–Specker (KS) contextuality. Why “non-“? Because a KS hypergraph violates the same condition X, however in a space of dimension n ≥ 3 in which all of its hyperedges must contain n vertices. In an n-dim non-KS hypergraph at least one hyperedge has less than n vertices.

If we represented vertices by vectors in a hypergraph, n mutually orthogonal vectors in each hyperedge would be indispensable for an experimental implementation of the hypergraph, KS or not. But although all of them are needed for an implementation, we can choose some smaller set of the vertices when considering contextuality for an application, say, for quantum computation or quantum communication. If the hypergraph with chosen reduced number of vertices violated the aforementioned condition X, it would be a non-KS hypergraph.

How to generate non-KS hypergraphs? A previous method of obtaining them was of exponential complexity and their generation in dimensions higher than eight faced a computational barrier. Therefore, in this paper, we make use of dimensional upscaling which does not scale with dimension. This enables us to generate non-KS hypergraphs in well over 32-dimensional Hilbert spaces. In the paper we give explicit examples for all spaces up to 16-dim ones and show that the minimal number of hyperedges fluctuates between eight (odd dimensions) and nine (even dimensions) under the requirement that at least one the hyperedges contains n vertices, all of which share at least two hyperedges.

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:

Objavljen rad u časopisu Applied Surface Science te prijavljen patent

Sorry, this entry is only available in Croatian. For the sake of viewer convenience, the content is shown below in the alternative language. You may click the link to switch the active language.

Znanstvenici Laboratorija za molekulsku fiziku i sinteze novih materijala IRB-a, doktorand Vlatko Gašparić mag. phys., dr. sc. Davor Ristić, dr. sc. Hrvoje Gebavi i dr. sc. Mile Ivanda objavili su u prestižnom časopisu Applied Surface Science (IF: 6.182) rad pod naslovom “Resolution and signal enhancement of Raman mapping by photonic nanojet of a microsphere”.

Fizičari objavili rad u časopisu Applied Surface Science te prijavili patent

U radu se po prvi puta primijenilo svojstvo tzv. fotonskog nanomlaza za pojačanje rezolucije i signala mapiranja u Ramanovoj spektroskopiji pomoću mehanički učvršćene mikrosfere, a konstruirana izvedba učvršćene mikrosfere prijavljena je i kao patent.

Ramanova spektroskopija nezaobilazna je metoda karakterizacije tvari u laboratoriju i na terenu, no zbog malog udarnog presjeka Ramanovog raspršenja, odziv je vrlo slabog intenziteta. Stoga su razvijene brojne metode pojačanja ove spektroskopske tehnike, od kojih je među najnovijima metoda koja koristi fotonski nanomlaz mikrosfere.

Fotonski nanomlaz (photonic nanojet – PNJ) izrazito je uzak i intenzivan snop svjetlosti koji nastaje uslijed obasjavanja dielektrične mikrosfere laserskim snopom ili ravnim valom svjetlosti. PNJ je zadobio pozornost znanstvenika od 2004. godine i našao je primjenu u raznim područjima. Da bi se iskoristio kao metoda pojačanja Ramanovog raspršenja pod mikroskopom, mikrosfere odgovarajućeg materijala i veličine potrebno je dovesti na površinu uzorka koji se istražuje te fokusirati upadni laserski snop iz mikroskopskog objektiva odgovarajuće širine i valne duljine kroz mikrosferu na uzorak.

Mikrosfere se deponiraju na uzorak kapanjem na podlogu, čime se njihove lokacije ne mogu kontrolirati. Međutim, na taj način moguće je prikupiti spektre samo izoliranih lokacija uzorka točno ispod mikrosfera.

Rad fizičara predstavlja novi pristup i izvedbeno rješenje u kontroliranju lokacije mikrosfere, na način da se mikrosfera pričvrsti na vrh stanjenog optičkog vlakna koje je stabilizirano drugim, okomito pričvršćenim stanjenim vlaknom, a pozicija se regulira mikropozicijskim podijima.

doktorand Vlatko Gašparić mag. phys., dr. sc. Davor Ristić, dr. sc. Hrvoje Gebavi i dr. sc. Mile Ivanda

doktorand Vlatko Gašparić mag. phys., dr. sc. Davor Ristić, dr. sc. Hrvoje Gebavi i dr. sc. Mile Ivanda

Inovacija je nazvana Two stemmed microsphere (TSMS). Korištenjem učvršćenja mikrosfere TSMS izvedbom, izbjegava se onečišćenje uzorka kapanjem tisuća mikrosfera, a mikrosferu je moguće dovesti na bilo koje mjesto na uzorku te održati pod upadnim snopom dok se uzorak pomiče. Drugim riječima, omogućuje se korištenje pojačanja fotonskog nanomlaza za ramansko mapiranje.

Rezultati istraživanja pokazali su tri puta bolju rezoluciju mapiranih površina, te četiri puta jači intenzitet signala spektara korištenjem TSMS-a s kvarcnom mikrosferom promjera 5 µm, u odnosu na isti eksperimentalni postav bez učvršćene mikrosfere. Eksperimentalna saznanja podržana su analitičkim simulacijama, za što su autori razvili računalni program na temelju Generalizirane Lorenz-Mie teorije upada laserske gausijanske zrake na mikrosferu. TSMS inovacija, te povezane varijante kontroliranja mikrosfere, prijavljene su i kao patent Državnom zavodu za intelektualno vlasništvo Republike Hrvatske.

Navedeni rezultati otvorili su novi put na području mapiranja u Ramanovoj spektroskopiji, čime je stvoren temelj za daljnje usavršavanje i usvajanje TSMS inovacije, kao i drugih inovacija za kontroliranje mikrosfere i upotrebe fotonskog nanomlaza.

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).