Mladen Pavičić
Quantum Information Theory
20011024
PROJECT PROPOSAL



Code: 
1.0 
Project Title: 





2.0 PRINCIPAL INVESTIGATOR
Principal investigator: 
President of the Scientific Council 
Dean or the Director of the Institution: 

Mladen Pavičić 
Prof. Željko Korlaet 
Prof. Željko Korlaet 
PROJECT PROPOSAL
6.0 PROJECT
6.1 
Major field: 

6.2 
Field: 

6.3 
Branch: 

6.4 
Research type: 

6.5 
Institution of emplyment: 
University of Zagreb, Faculty of Civil Engineering 
6.6 
Department: 
Department of Mathematics 
7.0 Keywords: 
quantum information theory, quantum entanglement, quantum computing, quantum logic, quantum logic gates, quantum communication, quantum computers, Hilbert lattices, Hilbert space, hypergraphs, quantum algorithms 
8.0 CONTACT

Name: 
Mladen 


Family name: 
Pavičić 


ZIP code: 
City: 


Fax: 




Email: 
pavicic@grad.hr 




Webaddress 


PROJECT COLLABORATORS
9.0 PRINCIPAL INVESTIGATOR
Code 
JMBG: 
Name: 
Family name: 
ID code: 
Scientific vocation 
Status: 
0082 
Mladen 
Pavičić 
RESEARCH DESCRIPTION
16.0 GOAL AND APPLICATION
16.3 Application of the research: 
The research will have its application in selecting physical effects and processes that are most suitable to serve as hardware of quantum computers, quantum communication, and ultimately quantum network. For, at the moment there are more than fifteen different physical implementations of quantum gates that handle qubits. An essential role in putting together main parts of quantum computers (quantum gate, register, processor, bus, storage devices, etc.) will play the quantum entanglement which will find its application not only in further development of theory and experiments of quantum computers and of quantum mechanics itself but also in quantum teleportation and in quantum communication theory and devices and in particular in quantum networks and cryptography. On the other hand, the development of the general algebra underlying quantum computation, which is often called quantum logic, will find its application not only in the quantum computation theory but also in the theory of Hilbert space, lattice theory, theory of Hilbert lattices, as well as in graph and hypergraph theory. In the end, elaboration of the interactionfree preparation of quantum qubits will find its application in handling and controlling quantum systems that must not be kicked out from their positions (trapped ions, BoseEinstein condensates). 
RESEARCH DESCRIPTION
17.0 CURRENT TRENDS AND THE RESEARCHER'S COMPETENCE
17.1 Background: 

Previous results of the researcher are integrated in the current trends in the field which is best reviewed in three recent books: Gruska, J.: Quantum Computing, Osborne McGrawHill, London (1999), Preskill, J: Quantum Information and Computation, http://theory.caltech.edu/~preskill/ph229/#lecture and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000). The proposal stresses three main aspects of the quantum information theory: entanglement (1), communication (2), and algorithms (3). Below, these points are illustrated by some previous contributions of the researcher:// (1) In (1.1) Pavicic, M. and J. Summhammer, Phys. Rev. Lett., 73, 3191 (1994) the researcher developed an entanglement and teleportation scheme based on fourphoton spin intensity interferometry independently of and at the same time with C. Bennett (IBM, USA) and A. Zeilinger (Innsbruck, Austria). For example, the scheme presented in (1.2) Pavicic, M., J. Opt. Soc. Am. B, 12, 821 (1995) is the scheme which was later on used in the famous teleportation experiment carried out in Innsbruck in 1998. The scheme was further elaborated in (1.3) Pavicic, M., Optics Comm., 142, 308 (1997). The entanglement elaborated in these paper serves as a basis for theoretical approach of entanglement of qubits in quantum computer schemes to be developed in the project; // (2) Quantum communication, quantum cryptography, quantum network, and partly controlling quantum computer gates are all mostly based on quantum optical devices (see e.g., Quantum Communication, Computing, and Measurement 2, Kumar, P, D'Ariano, and Hirota, O. (Eds.), Kluwer Academic, New York, 2000) and the researcher took an active part in the development of this fields. In (2.1) Pavicic, M., Phys. Rev. A 50, 34863491 (1994) it was discovered that there is a 100 percent correlation in polarization between two unpolarized photons subjected to simultaneous detection at a beam splitter. In (2.2) Paul, H. and Pavicic, M., Int. J. Theor. Phys., 35, 2085 (1996) the researcher combined the idea he put forward in his PhD in 1986 (alas, in Croatian  later it was independently elaborated by Elitzur, A. and Vaidman, L, Found. Phys., 23, 987 (1993)) with the detection scheme of H. Paul. In (2.3) Pavicic, M., Phys. Lett., A 223, 241 (1996) the researcher gave the first proposal of erasing interference fringes without transferring a single quant of energy to the system. This was soon afterwards experimentally verified by A. Karlsson and G. Bjoerk's group in the Royal Institute of Technology in Kista, Sweden. Further elaborations are presented in (2.4) Pavicic, M., Phys. Lett., A 224, 220 (1997), (2.5) Paul, H. and Pavicic, M., J. Opt. Soc. Am. B, 14, 12731277 (1997);// (3) All experiments leading towards quantum computing (Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin, 2000) and implicitly all existing algorithms (Pittenger, A. O.: An Introduction to Quantum Computing Algorithms, Birkhauser, Basel, 1999) rely on a recent result (Lloyd, S., Phys. Rev. Lett.,75, 346 (1995)  rigorously proved by Weaver, N., J. Math. Phys., 41, 240, (2000)) which shows that any quantum gate can be used to approximate any unitary transformation of a chosen Hamiltonian. Now, an open problem is how to formulate a general Hamiltonian which will eventually simulate any quantum system or process. Such a quantum simulator would require a general quantum algebra and the researcher paved the road towards it in a series of papers: (3.1) Pavicic, M. and Megill, N.D., Helv. Phys. Acta, 72, 189 (1999), (3.2) Pavicic, M., Int. J. Theor. Phys., 39, 813 (2000), (3.3) Pavicic, M., Fortschr. PhysikProgr. Physics, 48, 497 (2000), (3.4) McKay, B.D., Megill, N.D., and Pavicic, M., Int. J. Theor. Phys., 39, 2393 (2000), (3.5) Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 39, 2349 (2000). 
RESEARCH DESCRIPTION
17.2 Contination of the previous research: 

The researcher was the principal investigator of the previous project Quantum Computation and Quantum Communication (0082006). The proposed project would use the following results from the previous project: (1) the entanglement between two subsystems of a quantum systems that had no common past and that nowhere interacted with each other (1 in 17.1); (2) a loopholefree preselected Bell systems can be obtained by using nonmaximal singlet states (1 in 17.1); (3) an interactionfree control of quantum gates is possible (2 in 17.1); (4) new classes of quantum state equations (3 in 17.1). 
17.3: Citations, current application, patents: 

Number of citations in Science Citation Index (1996March 2001): 109 (101 journal papers, 8 proceedings papers). // D. R. Vij, ed. of Progress in Lasers Series at Kluwer Publishers, New York, offered the researcher to write a book on quantum information theory and experiments mid 2001; Contract for the book entitled Quantum Computation and Quantum Communication: Theory and Experiments signed Sept. 2001; // A. Karlsson and G. Bjoerk's group in the Royal Institute of Technology in Kista, Sweden carried out interactionfree experiments according to the researcher's schemes from references (see subsection 17.1 above): (2.2)  (2.5): Inoue, A.U., J. Optics B, 2, 338 (2000), Karlsson, A.U., Phys. Rev. Lett. 80, 1198 (1998), etc.;// A. Zeilinger's group in 1998 carried entanglement swapping and in effect the teleportation experiment using the same scheme as presented in Pavicic, M.,J. Opt.Soc.Am. B, 12, 821 (1995); Reviewed by Hariharan and Sanders, Progr. Optics XXXVI, p.1068 (1996). 
RESEARCH DESCRIPTION
18.0 PLAN, PROTOCOL AND METHODS
18.1: Hypothesis 

It is possible to use quantum logic (algebra of quantum logic gates) to give theoretical extrapolations of major experimental implementation of qubits (QED, NMR, ENDOR, etc) so as to verify their suitability for quantum registers, gates, processors, buses, repeaters, storage devices, etc. of the wouldbe quantum computers and decide on the most promising implementation. Quantum logic itself can be generalized (as an n dimensional Hilbert theory) so as to enable a construction of quantum simulator whose qubits would simulate a given quantum system. 
18.2 Meaning of the proposed research: 

The fact that one of the leading scientific publisher in the World (Kluwer, see 17.3 above) commissioned the book on some results of the proposed research in advance indicates its importance and meaning as well the researcher's merit for carrying it out. Billions of dollars which have recently been poured into the field as well the exponentially growing number of papers are other signs of its importance. It should be stressed here that not only the field of quantum computing and communication would benefit from the research. The new classes of quantum state equations will be a significant contribution to the Hilbert space theory as well as the theory of Hilbert lattices and hypergraph theory. On the other hand the quantum information theory especially through its elaboration of quantum entanglement offers a new insight into quantum mechanics and quantum optics and leads to many new applicable discoveries as has been well shown in the past ten years. 
18.3 Methods: 

To extrapolate experimental implementations of quibts the research will use Gruska, J.: Quantum Computing, Osborne McGrawHill, London (1999), Preskill, J: Quantum Information and Computation, http://theory.caltech.edu/~preskill/ph229/#lecture and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000) and the researcher's own elaboration of entanglement as given in Pavicic, M., J. Opt. Soc. Am. B, 12, 821 (1995) and his other papers. Elaboration of quantum communication, quantum cryptography, quantum network, and partly controlling quantum computer gates will start with mostly quantum optical methods as presented in Quantum Communication, Computing, and Measurement 2, Kumar, P, D'Ariano, and Hirota, O. (Eds.), Kluwer Academic, New York, 2000 and Bouwmeester, D., Ekert, A., and Zeilinger, A. (Eds): The Physics of Quantum Information, Springer Verlag, Berlin (2000) and the researcher's own contributions (1.3),(2.1)(2.5) as cited in subsection 17.1 above. To arrive at a generalized n dimensional quantum logic the research will start with Gruska, J.: Quantum Computing, Osborne McGrawHill, London (1999) and combine it with methods and algorithms developed in : Pavicic, M. and Megill, N.D., Helv. Phys. Acta, 72, 189 (1999), Pavicic, M., Int. J. Theor. Phys., 39, 813 (2000), Pavicic, M., Fortschr. PhysikProgr. Physics, 48, 497 (2000), McKay, B.D., Megill, N.D., and Pavicic, M., Int. J. Theor. Phys., 39, 2393 (2000), Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 39, 2349 (2000), Megill, N.D. and Pavicic, M., Int.J. Theor. Phys., 40, 1387 (2001) as well as with isomorphfree exhaustive generation of hypergraphs developed in McKay, B.D., J. Algorithms, 26, 306 (1998). 
RESEARCH DESCRIPTION
18.4 Protocol and program plan: 

First, the elaboration of a theoretical extrapolation of particular experimental implementations of quantum logic gates will be made. The ability of particular physical systems to carry out massive quantum calculation, keep coherence, stand error correction procedure, etc., will be estimated. Then the preliminary algorithms for constructing quantum state equations will be made. The algorithms will use the hypergraph theory as well as an isomorphfree exhaustive hypergraph generation. The obtained equations will in the end be used be used to give an n dimensional Hilbert lattice theory possibly not only as an approximation of the standard infinite dimensional Hilbert space but also a genuine quantum theory for quantum computers 

18.5 Expected results: 

Of the proposed theoretical extrapolation of particular experimental implementations of quantum logic gates is expected to decide on the most suitable physical implementations of quantum computers. New requests on coherence, error correction procedure, etc., are expected to emerge from the study and enable new experiments. Algorithms for constructing quantum state equations are first expected to give four and five atom in a block state which no one has succeed to obtain so far. Then, new classes of equations are expected to be found which would define an n dimensional Hilbert lattice theory. An immediate test for such a construct would be a generation of minimal and arbitrary KochenSpecker vectors which might then be experimentally verified. Also, the elaboration of laser control of qubits might give significant new effects in the field of quantum optical resonance. 
RESEARCH DESCRIPTION
18.6 Ethical norms and conformance to the Croatian legislation and international conventions: 

19.0 Notes: 

I am aware that it would be more proper to form a group of investigators. The reason why I am the only investigator is twofold. First, I am the only physicist at my faculty. Secondly, I am the only researcher in Croatia who is engaged in the field of quantum information theory, quantum computing, and quantum communication which are all rapidly growing fields in the world. 
20.0 List of 10 major scientific references of all researchers in the period between 1997 and 2001 
Pavicic, M., LoopholeFree Four Photon EPR Experiment, Physics Letters, A 224, 220226 (1997). 
Paul, H. and Pavicic, M., Nonclassical InteractionFree Detection of Objects in a Monolithic TotalInternalReflection Resonator, Journal of the Optical Society of America, B 14, 12731277 (1997). 
Pavicic, M., A Method for Reaching Detection Efficiencies Necessary for Optical LoopholeFree Bell Experiments, Optics Communications, 142, 308314 (1997). 
Paul, H. and Pavicic, M., Realistic InteractionFree Detection of Objects in a Resonator, Foundations of Physics, 28, 959970 (1998). 
Pavicic, M. and Megill, N.D., NonOrthomodular Models for Both Standard Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers, Helvetica Physica Acta, 72, 189210 (1999). 
Pavicic, M., Quantum Logic for Quantum Computers, International Journal of Theoretical Physics, 39, 813825 (2000). 
Pavicic, M., Quantum Simulators and Quantum Repeaters, Fortschritte der PhysikProgress of Physics, 48, 497503 (2000). 
Megill, N. D. and Pavicic, M., Equations, States, and Lattices of InfiniteDimensional Hilbert Spaces, International Journal of Theoretical Physics, 39, 23492391 (2000). 
McKay, B.D., Megill, N.D., and Pavicic, M., Algorithms for Greechie Diagrams, International Journal of Theoretical Physics, 39, 23932417 (2000). 
Pavicic, M., Quantum Logic for Genuine Quantum Simulators, in Donkor, E. and Pirich, A.R. (eds.), Quantum Computing, Proceedings of SPIE Vol. 4047 (2000); pp. 9096. 
PRINCIPAL INVESTIGATOR
21.0
JMBG: 
Name: 
Family name: 
ID code: 
Scientific vocation: 
Last appointment into vocation 
Mladen 
Pavičić 
Full Professor 

Year 
Institution 
Major field 
Field 
Branch 
Ph.D.: 
1986 
Physics Dept., Belgrade Univ. 
Natural sciences 
Physics 
Quant.Mech. 
Principal investigator role on the project: 

Employment and duties 
19791982 Assistant in Math. and Phys., Faculty of Civil Engineering, Department of Mathematics 
19821990, Scientific Assistant in Math. and Phys., University of Zagreb, Faculty of Civil Engineering, Dept. of Math. 
19901996, Assistant Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Dept. of Mathematics 
19962001, Associate Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Dept. of Mathematics 
19992000, Visiting Professor in Physics, University of Maryland Baltimore County, Baltimore, USA, Dept. of Phys. 
2001, Full Professor in Physics, University of Zagreb, Faculty of Civil Engineering, Department of Mathematics 
Education and specialisation 
19881990, University of Cologne, Germany, Institute for Theoretical Physics 
1993, June, Atomic Institute of the Austrian Universites, Vienna, Austria. 
1993, JulySeptember, Technical University of Berlin, Germany, Institute for Theoretical Physics. 
1994, AugustSeptember, Atomic Institute of the Austrian Universites, Vienna, Austria. 
1995, JuneOctober, HumboldtUniversity of Berlin, Germany, Department of NonClassical Radiation 
19992000, University of Maryland Baltimore County, Baltimore, USA, Dept. of Phys. 
Membership 
International Quantum Structure Association, Inc., Atlanta, Georgia, USA.; Member Founder 
HumboldtClub of Croatia, Zagreb, Croatia; President. 
European Physical Society 
Optical Society of America 
Awards 
Alexander von Humboldt Foundation Award: 19881990, University of Cologne, Germany, Institute for Theoretical Physics 
Alexander von Humboldt Foundation Award: 1993, Technical University of Berlin, Germany, Instit. for Theoretical Physics 
Alexander von Humboldt Foundation Award: 1995, HumboldtUniversity of Berlin, Germany, Dept.of NonClass.Radiation 
Senior Fulbright Teaching/Research Award:19992000, University of Maryland Baltimore County, USA, Dept. of Physics 
Ministry of Science and Technology of the Republic of Croatia