Doctoral School of Information Science and Technology

Budapest University of Technology and Economics (BUTE)

Faculty of Electrical Engineering and Informatics

Department of Telecommunications

Dr. IMRE, Sandor (DSc), Professor, Head of Department, Department of Telecommunications

Informational Geometric Solution to Additivity Problem of Quantum Channel Capacity

Introducing the research area

Additivity of quantum channels is still an exciting subject of current research. There are some quantum channels for which strict additivity is known, however, a general rule for quantum channels has not been verified yet. The additivity of quantum channels is still an open question and is currently under research. I deal with analyzing the additivity of the different quantum channel models, which have great importance in physical implementations and in optical communications. My researches also focus on analyzing information theoretic security of quantum cryptography using abstract information geometry objects.

Brief introduction of the research place

The Department of Telecommunications of Budapest University of Technology and Economics in Hungary has been providing a solid ground for teaching, researching and developing information and communication technologies for more than 60 years. The primary fields covered by the Department are acoustics, cryptography, computing (both classical and quantum), multimedia, networking and signal processing.

History and context of the research

In the information age that we live in, more than ever in history, we are facing the problem of exchanging data quickly and accurately. Although there are classical cryptographic schemes in theory which are unconditionally secure, in practice it is impossible to create unconditional security in classical modern cryptosystems. At the same time, the extrapolation of Moore’s Law leads us to conclude that we will be able to transcribe a single bit of information on an atom before 2017.

Quantum cryptographic protocols are designed with the intention that their security is guaranteed by the laws of quantum physics, therefore the security of the quantum-protocols will not be compromised by future developments in quantum computing.

The additivity of quantum channels is still a remarkable and valuable research field in quantum information theory and it could have deep relevance on future quantum communications. The additivity of some quantum channel models is known and it has been proved that strict additivity holds for all quantum channels. In my work, I analyze the additivity of various quantum channels. In physical applications, especially in the field of optical communications, however, the additivity of optical channels is still an open question.

Aim of the research

Quantum channel additivity is currently an active research area in quantum information theory. The additivity conjectures have emerged from an attempt to find a closed form expression for the capacity of a noisy quantum channel. Up till now, strict additivity for quantum channel capacity has been conjectured but not verified. My novel approach allows discussing open questions related to additivity of quantum channel capacities. The additivity property of quantum channels is still an exciting subject of current research. The accessible classical information from continuous quantum degrees of freedom is limited, the key issue behind the additivity of quantum channel capacity is the limitation of extractable information from quantum states. The equality of channel capacities is known for special cases, but the generalized rule is still unknown. There has been much progress toward describing the additivity property of quantum channels recently, however, there are still many open questions. 

In my works I analyze the additivity property and information theoretic security of quantum channels, using fast geometrical methods.

Methods

It has been proved in classical systems that the correlations between classical inputs do not increase the capacity of the classical channel. In quantum communication, the classical channel behavior can be achieved, if no correlation is allowed between the input states. In my method, I analyze the additivity of quantum channel capacity, and I would like to answer the question whether entangled states can increase the joint capacity of the tensor-product channel model.

In the course of my work I apply computational geometry in the quantum space between pure and mixed quantum states. With the help of efficient computational geometric methods, the additivity problem of quantum channels and the level of eavesdropping activity on the quantum channel can be computed and measured very efficiently. Computational geometry was originally focused on the construction of efficient algorithms and it provided a very valuable and efficient tool for solving difficult problems. The computation of the convex hull between quantum states cannot be computed efficiently by linear programming, however, the methods of computational geometry are better at solving these kinds of difficult problems. Computational geometry uses the results of classical geometry and the power of computing.

In my work I use the results of classical computational geometry to analyze the properties of quantum channels using current classical computer architectures. To analyze a quantum channel for a large number of input quantum states with classical computer architectures, very fast and effective algorithms are required. I plan to analyze the properties of quantum channels using the current classical computer architectures and the currently available most efficient algorithms. Currently the most efficient classical algorithms for this purpose are computational geometric methods. I use these classical computational geometric tools to analyze the still unknown or only conjectured properties of quantum channels, like the additivity of quantum channel capacities. I also use the methods of computational geometry to analyze the properties of quantum channels, however, quantum information serves as a distance measure instead of classical geometric distances.

Results

The results on quantum channel security and additivity property have been published in journals and at conferences (Princeton (New Jersey, USA); Harvard (Cambridge, USA); Queensland (Australia); London and Southampton (United Kingdom); Paris (France); Athens (Greece)).

I was given two Best Paper Awards at international conferences related to future computing and quantum information processing at University of Harvard, USA, and a Best Paper Award 2009 – "Pollak-Virag" – from the Scientific Association for Infocommunication (Hungary).

In my works I have shown that my geometrical approach on channel additivity and security could be a very efficient practical tool to answer still open questions related to quantum channel additivity and security.

My work proposes a new algorithm for computing the fidelity of an eavesdropper’s cloning machine. The proposed method uses quantum relative entropy to compute the smallest enclosing information ball. I have shown that a Delaunay triangulation based on quantum relative entropy plays an important role in a numerical calculation of the fidelity of quantum cloning machines. According to the proposed method, I compute the smallest enclosing ball based on Delaunay triangulation, which is considered to be a useful and efficient tool. I propose a new algorithm for computing the fidelity of quantum cloning transformation-based attacks in quantum cryptography and for estimating the security of a protocol. My geometrical security analysis is based on the allowed physical cloning transformations to the quantum state. My geometrical method can be applied to the main types of eavesdropping strategies, like incoherent, collective and coherent attacks.

In another study I present a fundamentally new algorithmic solution to the superactivation of zero-capacity quantum channels. Using my method, a larger set of “superactive” zero-capacity channels can be discovered very efficiently and the gap between theoretical and experimental results can be bridged. My algorithmic solution can be the key to finding other possible channel models and channel parameter domains, with possible combinations being proved by theory. If there are other combinations of channel models and channel probabilities that realize superactivation, my method can find them, however, I must analyze an extremely large set of input states, hence an extremely efficient algorithmic solution is required.

 

Expected impact and further research 

In my research, I analyze the additivity of quantum channel capacity and would like to answer the question whether entangled states can increase the joint capacity of the tensor-product channel model. My geometrical approach could be a very efficient practical tool to answer questions about quantum channel additivity that are still open.

In my future work on additivity analysis, I would like to extend my analysis to other quantum channel models and present an enhanced version of the proposed geometrical algorithm.

In a future work on superactivation of zero-capacity quantum channels, I would like to extend my results to other possible zero-capacity channels and show that these channels can also be superactive, using my abstract quantum-informational geometric objects.

The full list of publications and conferences can be found on my web page: www.hit.bme.hu/~gyongyosi/.

 

Publications, references, links

    List of Journal Publications

1. Laszlo Gyongyosi, Sandor Imre: Information Geometric Security Analysis of Differential Phase Shift QKD Protocol, Security and Communication Networks, John Wiley & Sons, Ltd. ISSN: 1939-0114; 2010, accepted

2. Laszlo Gyongyosi, Sandor Imre: Novel Quantum Information Solution to Copy-Protection and Secured Authentication, International Journal of Internet Technology and Secured Transactions (IJITST), ISSN (Online): 1748-5703, ISSN (Print): 1748-569X; 2010, accepted

3. Laszlo Gyongyosi, Sandor Imre: Quantum Informational Divergence in Quantum Channel Security Analysis, International Journal of Network Security, ISSN 1816-353X, ISSN 1816-3548; 2010, accepted

4. Laszlo Gyongyosi, Sandor Imre: Efficient Computational Information Geometric Analysis of Physically Allowed Quantum Cloning Attacks for Quantum Key Distribution Protocols, WSEAS TRANSACTIONS on COMMUNICATIONS, ISSN: 1109-2742; 2010, accepted

5. Laszlo Gyongyosi, Sandor Imre: Information Geometrical Approximation of Quantum Channel Security, International Journal On Advances in Security, Published by: International Academy, Research and Industry Association, ISSN: 1942-2636; 2010, accepted.

6. Laszlo Gyongyosi, Sandor Imre: Geometrical Estimation of Information Theoretical Impacts of Incoherent Attacks for Quantum Cryptography, International Review of PHYSICS, Print ISSN: 1971-680X; 2010, accepted

7. Laszlo Gyongyosi, Sandor Imre: Quantum Singular Value Decomposition Based Approximation Algorithm, Journal of Circuits, Systems, and Computers (JCSC), World Scientific, Print ISSN: 0218-1266, Online ISSN: 1793-6454; 2010, accepted

8. Laszlo Gyongyosi, Sandor Imre: Quantum Information Theoretical Based Geometrical Representation of Eavesdropping Activity on the Quantum Channel, Infocommunications Journal, Scientific Association for Infocommunications, ISSN 0018-2028; 2010, accepted

9. Laszlo Gyongyosi, Sandor Imre: Quantum Protected Software, International Review on Computers and Software, ISSN:1828-6003, 1828-6011; 2009, accepted

10. Laszlo Gyongyosi, Sandor Imre: Quantum cryptography based info-communication systems, Info-Communications Technology, Scientific Association for Infocommunications, BUTE, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, 2008. ISSN 0018-2028; Best Paper Award 2009 – "Pollak-Virag" – from the Scientific Association for Infocommunication (Hungary)

11. Laszlo Gyongyosi: Quantum information in data privacy, Alma Mater series, Studies on Information and Knowledge Processes: Open Data, Protected Data 2, pages 341–378., BUTE, Faculty of Economic and Social Sciences, ISSN 1587-2386, ISBN 798-963-87788-5-7; 2008

12. Laszlo Gyongyosi: TOR and Torpark: Functional and performance analyses of new generation anonymous browsers, Alma Mater series, Studies on Information and Knowledge Processes 11, pp. 159–191., BUTE, Faculty of Economic and Social Sciences, 2007. ISSN 1587-2386, ISBN-10 963-421-429-0, ISBN-13 987-963-421-429-8. Published on-line: Hungarian privacy Enhancing Technologies portal, web page: http://pet-portal.eu/

  Publications Under review

1. Laszlo Gyongyosi, Sandor Imre: Algorithmic Solution to Superactivation of Zero-Capacity Quantum Channels, IEEE Transactions on Information Theory

2. Laszlo Gyongyosi, Laszlo Bacsardi, Sandor Imre: Quantum Probabilistic Decisions for Intelligent Autonomic Networking and Communication, Nano Communication Networks, Elsevier

3. Sandor Szabo, Laszlo Gyongyosi, Sandor Imre: Performance Evaluation of Anycast-Based Micro-mobility Management, Computer Communications, Elsevier

  Book Chapters

1. L. Bacsardi, L. Gyongyosi, M. Bérces, S. Imre: Quantum Solutions for Future Space Communication, in "Quantum Computers", Nova Science Publishers, 2010

2. S. Szabo, L. Gyongyosi, K. Lendvai, S. Imre: Overview of IP Multimedia Subsystem Protocols and Communication Services, in "Advanced Communication Protocol Technologies: Solutions, Methods and Applications", 2010

  Conferences

1. Laszlo Gyongyosi, Sandor Imre: Information Geometrical Solution to Additivity of Non-Unital Quantum Channels, QCMC 2010, 10th Quantum Communication, Measurement & Computing Conference, Section on Quantum Computing and Quantum Information Theory (Centre for Quantum Computer Technology) July 2010, University of Queensland, Brisbane, Queensland, Australia, accepted

2. Laszlo Gyongyosi, Sandor Imre: Computational Information Geometric Analysis of Quantum Channel Additivity, Photon10 Conference, Quantum Electronics Group, Section on Quantum information, University of Southampton, Institute of Physics (IOP) Optics and Photonics Division, 2010, Southampton, UK, accepted

3. Laszlo Gyongyosi, Sandor Imre: Novel Geometrical Solution to Additivity Problem of Classical Quantum Channel Capacity, The 33rd IEEE Sarnoff Symposium – 2010, IEEE Princeton/Central Jersey Section, Princeton University, Apr. 2010, Princeton, New Jersey, USA, accepted

4. Laszlo Gyongyosi, Sandor Imre: Computational Geometric Analysis of Physically Allowed Quantum Cloning Transformations for Quantum Cryptography, 4th WSEAS International Conference on COMPUTER ENGINEERING and APPLICATIONS, Section on Quantum Computing, (The World Scientific and Engineering Academy and Society, CEA '10), 2010, University of Harvard, Cambridge (Massachusetts), USA., accepted. BEST PAPER AWARD 2010, Harvard University, Cambridge, USA

5. Laszlo Bacsardi, Laszlo Gyongyosi, Sandor Imre: Using Redundancy-free Quantum Channels for Improving the Satellite Communication, PSATS 2010, 2nd International ICST Conference on Personal Satellite Services, Section on Satellite Quantum Communications, 4–6 February 2010, Rome, Italy, accepted

6. Laszlo Gyongyosi, Sandor Imre: Quantum Informational Geometry for Secret Quantum Communication, The First International Conference on Future Computational Technologies and Applications, FUTURE COMPUTING 2009, Section on Quantum Computing, International Academy, Research and Industry Association, 2009, Athens, Greece, accepted. FUTURE COMPUTING 2009: Best Paper Award

7. Laszlo Gyongyosi, Laszlo Bacsardi, Sandor Imre: Novel Approach for Quantum Mechanical Based Autonomic Communication, The First International Conference on Future Computational Technologies and Applications, FUTURE COMPUTING 2009, Section on Quantum Computing, International Academy, Research and Industry Association, 2009, Athens, Greece, accepted

8. Laszlo Bacsardi, Laszlo Gyongyosi, Sandor Imre: Solutions For Redundancy-free Error Correction In Quantum Channel, International Conference on Quantum Communication and Quantum Networking, 26–30 October, 2009, Vico Equense, Sorrento peninsula, Naples, Italy, accepted

9. Laszlo Gyongyosi, Sandor Imre: Quantum Divergence based Quantum Channel Security Estimation, N2S’2009 International Conference on Network and Service Security, Section on Quantum Cryptography and QKD, IFIP TC6 WG, IEEE France, June, 2009, Paris, France, accepted

10. Laszlo Gyongyosi, Sandor Imre: Unduplicable Quantum Data Medium Based Secret Decryption and Verification, The 4th International Conference for Internet Technology and Secured Transactions (ICITST-2009), 9–12 November, 2009, IEEE UK & RI, London, United Kingdom, accepted

11. Laszlo Gyongyosi, Sandor Imre: Fidelity Analysis of Quantum Cloning Attacks in Quantum Cryptography, ConTEL 2009 International Conference on Telecommunications, IEEE Communications Society, 2009, Zagreb, Croatia, accepted

12. Laszlo Gyongyosi: Really unbreakable? The Security Analysis of Quantum Cryptography, Hacktivity conference 2008, Budapest

13. Laszlo Gyongyosi: Quantum copy-protection based on holographic data storage, BUTE, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, 2008

14. Laszlo Gyongyosi: Quantum Computation in computer network attacking, BUTE, Department of Measurement and Information Systems, Search-Lab, 2007

15. Laszlo Gyongyosi: The holographic quantum copy-protection protocol, BUTE, Faculty of Electrical Engineering and Informatics, Scientific Students Association 2007, Special award of the Scientific Students Association, BUTE

16. Laszlo Gyongyosi: A technical breakthrough in prime factorization, BUTE, Faculty of Electrical Engineering and Informatics, Scientific Students Association 2007, Special award of the Scientific Students Association, BUTE

17. Laszlo Gyongyosi: Simulation of the perfect quantum based key agreement, National Scientific Students Association, OTDK 2007, Award of the Hungarian Scientific Students Association of Computer Science and Information Technology

18. Laszlo Gyongyosi: Simulation of the perfect quantum based key agreement, BUTE, Faculty of Electrical Engineering and Informatics, Scientific Students Association, 2006, 1st prize (Ericsson Hungary)

19. Laszlo Gyongyosi: Formal Analysis of Quantum Cryptography, BUTE, Faculty of Electrical Engineering and Informatics, Scientific Students Association, 2006, 3rd prize

    Reviewer

• IEEE Transactions on Computers, IEEE Computer Society, ISSN 0018-9340.

• Computers & Electrical Engineering, Elsevier Ltd., ISSN: 0045-7906.

• Security and Communication Networks, John Wiley & Sons, Ltd.

• Computer and Network Security, ICADIWT Conference, IEEE UK & RI, London, United Kingdom

    Scientific research projects

• Analysis of Ring based Real-time Call Admission Control, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Performance Evaluation of Anycast-Based Micro-mobility Management, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Real-time Identification of RFID Microchip Implants, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Voice Directed Picking Systems and Advanced Indoor Communication Methods, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Impacts of IMS QoS Parameters on Multimedia Telephony Service Quality, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Adaptive Distance Estimation and Real-Time Indoor Localization using RSSI Measures, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Automated FoIP and VoIP Testing, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Optimal Algorithms for Real-Time Object Tracking and Locating, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Network Security Analysis and Protection of Embedded Systems in Virtual Private Networks, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Design and Implementation of Wireless MESH Network with Mobility Support, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Accurate Mobility Modeling and Location Prediction in Mobile Networks, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Development of Attentive and Zero Input User Interface in Mobile Environment, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

• Fixed-Mobile Convergence based Location and Availability Service with IMS, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre, T-Com

• Performing WLAN SSID based Presence and Location Service in NGN Wireless Communication Systems, Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics, Department of Telecommunications, Mobile Communications and Computing Laboratory, Mobile Innovation Centre

Teaching activity

Quantum Computing and Communications

Measuring Laboratory (Informatics and Electrical Engineering)

 Awards

• BEST PAPER AWARD 2010, 4th WSEAS International Conference on COMPUTER ENGINEERING and APPLICATIONS, Harvard University, Cambridge, USA

• FUTURE COMPUTING 2009: Best Paper Award, The First International Conference on Future Computational Technologies and Applications, 2009

• Best Paper Award 2009 – "Pollak-Virag" – from the Scientific Association for Infocommunication (Hungary)

• Republican Scholarship

• Professional Scholarship, Faculty of Electrical Engineering and Informatics, BUTE (A-level, highest category)

• University Professional Scholarship, BUTE (A-level, highest category)

Short C.V.

László Gyöngyösi, Ph.D Student since 2008, Budapest University of Technology and Economics. He received the M.Sc. degree in Computer Science with Honors from the Technical University of Budapest in 2008. His research interests are in Quantum Computation and Communication, Quantum Cryptography and Quantum Information Theory.