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.

Ostvareno generiranje parova polarizacijski spregnutih fotona

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Sa zadovoljstvom objavljujemo da je 9. travnja 2018. istraživači Istraživačke jedinice Fotonika i kvantna optika Znanstvenog centra izvrsnosti za napredne materijale i senzore, na Institutu Ruđer Bošković, dovršili su gradnju eksperimentalnog postava izvora parova spregnutih fotona zasnovanog na procesu spontane parametarske pretvorbe (Engl. spontaneous parametric downconversion (SPDC), kolinearni proces tipa II) fotona valne duljine 405 nm u parove infracrvenih fotona u PPKTP kristalu te optičkom postavu u Sagnac-ovoj konfiguraciji. Izvor stabilno generira koincidentne parove polarizacijski spregnutih fotona.

Iako je kvantno sprezanje fotona poznato, ovaj kontraintuitivni efekt i dalje je predmet intenzivnog istraživanja kako na fundamentalnoj tako i na razini mogućih primjena u kvantnoj komunikaciji, kvantnom računanju i kvantnoj metrologiji. Ostvareni rezultat je ključan za buduća istraživanja ove grupe.

Arbitrarily exhaustive generation of contextual sets

Recently obtained results published in Pavičić, M., Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets, Physical Review A, 95, 06212–1-25 (2017) will be implemented in a series of experiments in the CEMS Research Unit Photonics and Quantum Optics.

Quantum contextuality is a property of quantum systems not to have predetermined values of their observables, in contrast to classical systems. Take an entangled photon pair. Each of the photons is genuinely unpolarized before we let them through polarizers.  After polarizers, measurements find the photons in definite polarization states. Can we assume that these polarizations were somehow predetermined when the pair was created? The so-called contextual sets of states of photons prove that we cannot. Such sets are not of just of a foundational theoretical interest. Recently, it turned out that the “contextuality is the source of a quantum computer’s power” (Nature; cited in the paper). Therefore, it is important for future applications and implementations to find new classes, instances, and structure of contextual sets as well as to design algorithms and programs for obtaining them. In this paper, arbitrary exhaustive hypergraph-based generation of the most explored contextual sets, Kochen-Specker (KS) ones, is carried out in up to 32 dimensions.

Twelve classes of critical KS sets (the ones that cannot be simplified further) are generated and analyzed, huge number of novel types and instances of them obtained and numerous properties of theirs found. Several thousand times more types and instances of KS sets than previously known are generated. All KS sets in three of the classes and in the upper part of a fourth are novel. The generation was carried out with the help of McKay-Megill-Pavičić (MMP) hypergraph language, algorithms, and programs which generate KS sets (see the feature image for two hypergraphs of 8-dim KS sets; also the figure below) strictly following their definition from the Kochen-Specker theorem, which itself celebrates semicentennial this year. This is in contrast to parity proof based algorithms which prevail in the literature and for which the majority of KS sets and even a whole KS class (as the one shown in the Figure below) are simply invisible.

Priopcenje za javnost povodom opstruiranja financiranja iz EU fondova od strane MZOS-a

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PRIOPĆENJE ZA JAVNOST Zagreb, 7. lipnja 2016.

Otvoreno pismo ministru znanosti, obrazovanja i sporta Predragu Šustaru:

Opstruiranjem financiranja iz EU fondova hrvatskih znanstvenih centara izvrsnosti ugrožava se 50 milijuna eura iz strukturnih fondova i radna mjesta za hrvatske znanstvenike – traži se hitna reakcija ministra Šustara!

Pedeset milijuna eura, upitna radna mjesta za čak tri stotine doktoranada i postdoktoranada, te riskiranje penala od Europske komisije, samo su dio crne statistike koja ozbiljno prijeti Republici Hrvatskoj (RH), a odvija se u sjeni problema s kurikularnom reformom.

Deset znanstvenih centara izvrsnosti proglašenih od strane Ministarstva znanosti obrazovanje i sporta (MZOS) tijekom 2014. i 2015. godine na prijedlog Nacionalnog vijeća za znanost, visoko obrazovanje i tehnološki razvoj, posljednjih su nekoliko mjeseci postalo taocem MZOS-a.

Naime, RH se strateški odredila kroz Operativni program (OP) za financiranje Znanstvenih centara izvrsnosti (2014 – 2020), te se prema Operativnom programu očekuje 50 milijuna eura iz Europskog fonda za regionalni razvoj (ERDF) koji bi bili na raspolaganju proglašenim centrima.

Kako bi centri mogli iskoristiti europska sredstva, MZOS je obvezan raspisati natječaj. Prvi indikativni rok za raspisivanje natječaja bio je 31. ožujka, te je pomaknut na 1. lipnja 2016., a natječaj još nije raspisan.

Unatoč brojnim službenim molbama za poštivanjem obveza koje su voditelji Znanstvenih centara izvrsnosti posljednjih mjeseci dostavili ministru Šustaru i premijeru Oreškoviću s upozorenjem da je RH preuzela obvezu te je dužna raspisati planirani natječaj iz strukturnih fondova u sklopu kojih bi se izvršila evaluacija planiranih troškova u okviru pojedinih centara, s današnjim datumom MZOS još uvijek nije aktivirao natječaj Europskog fonda za regionalni razvoj (ERDF) koji bi omogućio povlačenje čak 50 milijuna eura za Znanstvene centre izvrsnosti. Time se ozbiljno ugrožava realizacija znanstvenih aktivnosti proglašenih ZCI-a i gubitak 50 milijuna eura iz EU te zapošljavanje 300 mladih stručnjaka.

Podsjetimo, MZOS je proglasio Znanstvene centre izvrsnosti iz područja prirodnih, biomedicinskih, biotehničkih i tehničkih znanosti nakon zahtjevnih kriterija javnog natječaja, uključujući opsežne domaće i međunarodne recenzije i intervjue s voditeljima predloženih centara koji su proveli Agencija za znanost i visoko obrazovanje (AZVO) i Nacionalno vijeće za znanost, visoko obrazovanje i tehnološki razvoj. MZOS je potom temeljem članka 29. stavka 2. Zakona o znanstvenoj djelatnosti i visokom obrazovanju (Narodne novine, broj: 123/2003, 105/2004, 174/2004, 2/2007 – Odluka Ustavnog suda Republike Hrvatske, 46/2007, 45/2009,63/2011,94/2013, 139/13 i 101/2014 – Odluka i Rješenje Ustavnog suda Republike Hrvatske) proglasilo znanstvene centre izvrsnosti RH, čiji su članovi izvrsni hrvatski znanstvenici, među nositeljima međunarodne prepoznatljivosti hrvatske znanosti.

Proces prijave, vrednovanja i odabira centara trajao je tri godine, a Vlada RH je nakon provedenog postupka recenzija uskladila program centara s nacionalnim prioritetima i oni su u skladu sa Strategijom pametne specijalizacije (S3). Ovu Strategiju su više od dvije godine izrađivali brojni eksperti iz javnog i privatnog sektora koji se bave istraživanjem i razvojem, te ju je usvojio Hrvatski sabor i Europska komisija za znanost.

Cilj proglašenja centara je bio omogućiti izvrsnim hrvatskim znanstvenicima i institucijama uvjete za vrhunski istraživački rad kroz stabilno i pojačano financiranje te edukaciju mladih znanstvenika i značajan doprinos gospodarstvu RH.

Slijedom navedenog, proizlazi da se nepoštivanjem zadanih obveza od strane MZOS-a te neprovođenjem preuzetih obveza direktno ugrožavaju nacionalni interesi.

Nažalost, jedan od glavnih protivnika ustroja hrvatskih centara izvrsnosti, kao i od strane Europske komisije usvojene pametne specijalizacije (S3) RH, a koja je jedan od glavnih preduvjeta za povlačenje sredstava iz strukturnih fondova, je pomoćnik ministra za znanost dr. sc. Krešimir Zadro.

Poštovani ministre Šustar, otvorenim pismom javnosti obraćamo Vam se ispred svih Znanstvenih centara izvrsnosti (ZCI) iz područja prirodnih, biomedicinskih, biotehničkih i tehničkih znanosti sa zahtjevom da se javno očitujete o razlozima nepoštivanja odluka Vlade RH i neprovođenju usvojenih programa financiranja hrvatskih centara izvrsnosti iz EU fondova te datumu raspisivanja natječaja kako bi se izbjegao crni scenarij.

Vjerujemo da niste spremni potpuno ignorirati izvrsne hrvatske znanstvene skupine i propustiti priliku da se kroz usvojeni program pametne specijalizacije povuku sredstva u iznosu od 50 milijuna eura iz strukturnih fondova.

U situaciji kad se domaća sredstva za znanost i istraživanje sustavno režu, kad se događa egzodus najboljih mladih obrazovanih stručnjaka, znanstvena istraživanja i inovacije preživljavaju velikim dijelom zbog izvrsnosti istraživačkih skupina i velikih napora znanstvenika u povlačenju sredstva iz programa Europske unije, ovakvo opstruiranje rada Znanstvenih centara izvrsnosti da osiguraju europska sredstva za rad i zapošljavanje stručnog kadra je nedopustivo!

S poštovanjem,
voditelji proglašenih Znanstvenih centara izvrsnosti (STEM područja):

Znanstveni centar izvrsnosti za napredne materijale i senzore,
Institut Ruđer Bošković i Institut za fiziku, Zagreb

Dr. sc. Milko Jakšić –
Dr. sc. Mile Ivanda –
Dr. sc. Mario Stipčević –
Dr. sc. Marko Kralj –

Znanstveni centar izvrsnosti za reproduktivnu i regenerativnu medicinu,

Medicinski fakultet, Sveučilište u Zagrebu,
Akademik prof. Slobodan Vukičević –
Prof. dr. sc. Davor Ježek –

Znanstveni centar izvrsnosti za virusnu imunologiju i cjepiva,
Medicinski fakultet, Sveučilište u Rijeci
Prof. dr. sc. Stipan Jonjić –

Znanstveni centar izvrsnosti za znanost i tehnologiju – STIM, Sveučilište u Splitu
Prof. dr. dr. h.c. Vlasta Bonačić-Koutecky –

Znanstveni centar izvrsnosti za bioraznolikost i molekularno oplemenjivanje bilja, Agronomski fakultet , Sveučilište u Zagrebu
Prof. dr. sc. Zlatko Šatović –

Znanstveni centar izvrsnosti za bioprospecting mora
Institut Ruđer Bošković, Zagreb Rozelindra Čož-Rakovac –

Znanstveni centar izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri, Prirodoslovno-matematički fakultet, Sveučilište u Zagrebu Hrvoje Buljan –
Prof. dr. sc. Pavle Pandžić –

Znanstveni centar izvrsnosti za personaliziranu brigu o zdravlju,

Sveučilište Josip Juraj Strossmayer u Osijeku
Prof. dr. sc. Gordan Lauc –
Prof. dr. sc. Ines Drenjančević –

Znanstveni centar izvrsnosti za temeljnu, kliničku i translacijsku neuroznanost, Medicinski fakultet, Sveučilište u Zagrebu
Prof. dr. sc. Miloš Judaš –

Znanstveni centar izvrsnosti za znanost o podatcima i kooperativne sustave, Fakultet elektrotehnike i računarstva, Sveučilište u Zagrebu Sven Lončarić –
Prof. dr. sc. Ivan Petrović –

Priopćenje voditelja proglašenih
            Znanstvenih centara izvrsnosti (STEM područja)             ___________________________________________________________________________________________________

Physics of the Dark Universe Paper “KWISP: An ultra-sensitive force sensor for the Dark Energy sector”

One of the remaining puzzles in physics is the composition of the Universe. Now days we believe that it is made of about 5% ordinary matter, 25% dark matter and 70% of dark energy. Our knowledge about the nature of the dark constituents of the Universe is very feeble. They were introduced to explain some observational data. In particular the dark energy was introduced to explain the observed acceleration in the expansion rate of the Universe. One of the possible mechanisms would be the existence of a light scalar field. To render it compatible with General Relativity in the solar system and “fifth force” searches on Earth they have to be screened. One possibility is a so called “chameleon” mechanism which renders their effective mass dependent on the local matter density. In case they exist they can be produced in the Sun and detected on Earth by a suitable sensor. The detection mechanism relies on the equivalent of the radiation pressure, where solar chameleons impinge on a mobile surface and transfer momentum to it which displaces it from the equilibrium position.


Such a sensor has been built and tested in cooperation with the optics laboratory at INFN Trieste where the sensor was situated before transferring it to the final setup at CERN which was noted in the CERN Courier article (see picture). It is based on a thin silicon nitride micro-membrane placed inside a Fabry–Perot optical cavity. By monitoring the cavity characteristic frequencies it is possible to detect the tiny membrane displacements caused by an applied force. Its application to experiments in the Dark Energy sector, such as those for Chameleon-type WISPs, is particularly attractive, as it enables a search for their direct coupling to matter. The sensitivity and the absolute force calibration are given in the article published in the journal Physics of the Dark Universe (impact factor 8.57).




9. Feasibility Study for employing the uniquely powerful ESS linear accelerator to generate an intense neutrino beam for leptonic CP violation discovery and measurement (ESSnuSB), leader for Croatia: B. Kliček. Project No.  777419 (H2020), signed: 22.11.2017., started: 01.01.2018. Financed through Horizon 2020.

8. “Support for top-level research of Centre of excellence for advanced materials and sensing devices“, leaders M. Jakšić, M. Ivanda, M. Kralj, and M. Stipčević. Funded through European structural and 5nvestment funds (ESIF), MSE grant No. KK.

7.  COST action CA15139 – Combining forces for a novel European facility for neutrino-antineutrino symmetry-violation discovery (EuroNuNet), Action chair: Dr Marcos Dracos (IN2P3 Strasbourg, France), Management Committee Member: Dr Budimir Kliček (Ruđer Bošković Institute, Zagreb, Croatia)

6. “Quantum entanglement for ultra-secure communications“, Leaders: Dr. Mario Stipčević, (CEMS-IRB, Zagreb, Croatia) and Prof. dr. Rupert Ursin (IQOQI, Vienna, Austria). Duration: 2016-2017 (2 years). In this project we address scientific and technological aspects of quantum entanglement which lies in the heart of the secure information exchange, quantum cryptography, random number generation as well as some vibrant scientific research topics related to quantum information and secure communications.

5. “Holography and interferometry under weak illumination” HrZZ – IP-2014-09-7515, 01.05.2015. – 30.04.2019. Leader: Nazif Demoli, Institute of Physics (IF). Associates: Hrvoje Skenderović (IF), Davorin Lovrić (IF), Jadranko Gladić (IF), Mario Rakić (IF), Mario Stipčević (RBI), Ognjen Milat (IF), Mladen Pavičić, Denis Abramović (IF), Marin Karuza (University of Rijeka). Research areas: Optical physics.

4. “TRANSHOW1 Knowledge transfer“, leader M. Lončarić.

3. COST Action MP1406 – Multiscale in modelling and validation for solar photovoltaics (MultiscaleSolar), Action Chair: Dr James Connolly (Génie électrique et électronique de Paris), Management Committee Member: Dr Martin Lončarić, (Ruđer Bošković Institute, Zagreb, Croatia)

2. “ICT COST Action IC1306 Cryptography for Secure Digital Interaction“, Leader: Prof. Claudio Orlandi (Aarhus University, Denmark), Coordinator for Croatia: Dr. Mario Stipčević, Ruđer Bošković Institute.

1. “ICT COST Action CA15220 Quantum Technologies in Space“, Leader: Prof. Angelo Bassi (University of trieste, Italy), Coordinator for Croatia: Dr. Mario Stipčević, Ruđer Bošković Institute

Sci Reports published paper on optical quatnum random number generator

On-Demand Optical Quantum Random Number Generator with Ultra-Fast Response

The study was published by online journal Scientific Reports (IF 5.578) of the Nature Publishing Group.

Mario Stipčević from the Ruđer Bošković Institute (RBI) and his colleague Rupert Ursinfrom the Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, developed a new model of a quantum random number generator (QRNG). This device provides an ultra-fast response upon a bit request (9.8 ns) with 100 percent efficiency upon the trigger, and in-future-of-request random action. None of the generators or generating principles known so far satisfied all those requirements simultaneously to that extent.

On-Demand Optical Quantum Random Number Generator with Ultra-Fast Response

The device works on the principle similar to a coin toss bearing in mind that the process of flipping and reading a coin takes a very short time and the coin never flips away from your hands. With a given state of technology this new QRNG could be reduced to the size of the chip, which would open opportunities for a wide range of applications. This study was published by online journal Scientific Reports (IF 5.578) of the Nature Publishing Group.

Digital data processing in computers, mobile devices or ATM machines has a huge impact on our modern information-based society. Random numbers are essential for cryptographic protocols which are necessary to ensure security, privacy and integrity of communicated data.

Random number generators are essential components for a wide range of applications such as: cryptographic data protection, scientific research, simulations, or real and virtual casinos and online games. For example, in security systems they provide secret keys or tokens for authentications and encryption. They are commonly classified by the source of their randomness.

Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms, but rather on a physical process to provide true randomness, which means that physical random numbers generators derive random numbers from a physical source of reasonably random process e.g. flipping a coin. This makes them more reliable, since their behaviour could not be replicated in a reasonable amount of time as in the case of pseudo-random generators.

”However, our primary motivation in this study was solving the fundamental problems of quantum entanglement.” – explained Stipčević, a senior research associate in the RBI Laboratory for electromagnetic and weak interactions and Head of the Research Unit for Photonics and Quantum Optics of the Center of Excellence for Advanced Materials and Sensors (CEMS).

MStipcevic - RUrsin

In this paper titled: “An On-Demand Optical Quantum Random Number Generator with In-Future Action and Ultra-Fast Response” the scientists presented a conceptually simple implementation, which offered a 100 percent efficiency of producing a random bit upon a request and simultaneously exhibited an ultra-low latency.

”We presented a novel type of QRNG which randomness can be obtained by suitable tuning the device controllable parameters in function of the hardware imperfections. It is unique in simultaneously satisfying three characteristics: a very short latency between the random bit request signal and the moment when the bit is generated, all physical processes relevant to generation of a bit happen after the request signal and with a 100 percent efficiency of producing a bit upon a request.

On top of that, we estimated deviation of the QRNG from perfect randomness and demonstrated that generated sequences of random bits pass NIST Statistical Test Suite (STS)1 without post-processing.” – concluded Stipčević and Ursin.