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  • 1.
    Abidin, Aysajan
    et al.
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Larsson, Jan-Åke
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Direct proof of security of Wegman-Carter authentication with partially known key2014In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 13, no 10, p. 2155-2170Article in journal (Refereed)
    Abstract [en]

    Information-theoretically secure (ITS) authentication is needed in Quantum Key Distribution (QKD). In this paper, we study security of an ITS authentication scheme proposed by Wegman& Carter, in the case of partially known authentication key. This scheme uses a new authentication key in each authentication attempt, to select a hash function from an Almost Strongly Universal2 hash function family. The partial knowledge of the attacker is measured as the trace distance between the authentication key distribution and the uniform distribution; this is the usual measure in QKD. We provide direct proofs of security of the scheme, when using partially known key, first in the information-theoretic setting and then in terms of witness indistinguishability as used in the Universal Composability (UC) framework. We find that if the authentication procedure has a failure probability ε and the authentication key has an ε´ trace distance to the uniform, then under ITS, the adversary’s success probability conditioned on an authentic message-tag pair is only bounded by ε +|Ƭ|ε´, where |Ƭ| is the size of the set of tags. Furthermore, the trace distance between the authentication key distribution and the uniform increases to |Ƭ|ε´ after having seen an authentic message-tag pair. Despite this, we are able to prove directly that the authenticated channel is indistinguishable from an (ideal) authentic channel (the desired functionality), except with probability less than ε + ε´. This proves that the scheme is (ε + ε´)-UC-secure, without using the composability theorem.

  • 2. Dang, Hoan Bui
    et al.
    Blanchfield, Kate
    Stockholm University, Faculty of Science, Department of Physics.
    Bengtsson, Ingemar
    Stockholm University, Faculty of Science, Department of Physics.
    Appleby, D. M.
    Linear Dependencies in Weyl-Heisenberg Orbits2013In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 12, no 11, p. 3449-3475Article in journal (Refereed)
    Abstract [en]

    Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which arises from the torsion points of a certain elliptic curve). This connection with elliptic curves is signalled by the presence of linear dependencies among the SIC vectors. Here we look for analogous connections between SICs and algebraic geometry by performing computer searches for linear dependencies in higher dimensional SICs. We prove that linear dependencies will always emerge in Weyl-Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix. This includes SICs when the dimension is divisible by 3 or equal to 8 mod 9. We examine the linear dependencies in dimension 6 in detail and show that smaller dimensional SICs are contained within this structure, potentially impacting the SIC existence problem. We extend our results to look for linear dependencies in orbits when the fiducial vector lies in an eigenspace of other elements of the Clifford group that are not order 3. Finally, we align our work with recent studies on representations of the Clifford group.

  • 3.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Multipartite quantum systems and symplectic toric manifolds2011In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 10, no 2, p. 257-269Article in journal (Refereed)
    Abstract [en]

    In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We also investigate entangled multipartite states based on moment map and Delzant's construction of toric manifolds and algebraic toric varieties.

  • 4.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant2010In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 9, no 2, p. 233-238Article in journal (Refereed)
    Abstract [en]

    In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant S-(m)(2) of the multi-local Lorentz-group SL(2, C)(circle times m). Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase.

  • 5.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant2009In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 9, no 2, p. 233-238Article in journal (Refereed)
    Abstract [en]

    In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant S(m)2S2(m) of the multi-local Lorentz-group SL(2, \mathbbC)ÄmSL(2C)m  . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase

  • 6.
    Johansson, Niklas
    et al.
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering.
    Larsson, Jan-Åke
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering.
    Efficient classical simulation of the Deutsch-Jozsa and Simons algorithms2017In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 16, no 9, article id UNSP 233Article in journal (Refereed)
    Abstract [en]

    Along-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch-Jozsa and Simons problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch-Jozsa problem with probability 1 using only one oracle query, and Simons problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch-Jozsa and Simons problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.

  • 7.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.
    Can Quantum Information be Processed by Macroscopic Systems?2007In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 6, no 6, p. 401-429Article in journal (Refereed)
    Abstract [en]

    We study the problem: Can Quantum Information be Processed by Macroscopic Systems?

  • 8. Kish, Laszlo B.
    et al.
    Granqvist, Claes-Göran
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    On the security of the Kirchhoff-law-Johnson-noise (KLJN) communicator2014In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 13, no 10, p. 2213-2219Article in journal (Refereed)
    Abstract [en]

    A simple and general proof is given for the information theoretic (unconditional) security of the Kirchhoff-law-Johnson-noise key exchange system under practical conditions. The unconditional security for ideal circumstances, which is based on the second law of thermodynamics, is found to prevail even under slightly non-ideal conditions. This security level is guaranteed by the continuity of functions describing classical physical linear, as well as stable non-linear, systems. Even without privacy amplification, Eve's probability for successful bit guessing is found to converge toward 0.5-i.e., the perfect security level-when ideal conditions are approached.

  • 9.
    Pacher, Christoph
    et al.
    Department of Safety & Security, AIT Austrian Institute of Technology, Austria.
    Abidin, Aysajan
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Lorünser, Thomas
    Department of Safety & Security, AIT Austrian Institute of Technology, Austria.
    Peev, Momtchil
    Department of Safety & Security, AIT Austrian Institute of Technology, Austria.
    Ursin, Rupert
    Institut für Experimentalphysik, Universität Wien, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Austria.
    Zeilinger, Anton
    Institut für Experimentalphysik, Universität Wien, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Austria.
    Larsson, Jan-Åke
    Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, The Institute of Technology.
    Attacks on quantum key distribution protocols that employ non-ITS authentication2016In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 15, no 1, p. 327-362Article in journal (Refereed)
    Abstract [en]

    We demonstrate how adversaries with unbounded computing resources can break Quantum Key Distribution (QKD) protocols which employ a particular message authentication code suggested previously. This authentication code, featuring low key consumption, is not Information-Theoretically Secure (ITS) since for each message the eavesdropper has intercepted she is able to send a different message from a set of messages that she can calculate by finding collisions of a cryptographic hash function. However, when this authentication code was introduced it was shown to prevent straightforward Man-In-The-Middle (MITM) attacks against QKD protocols.

    In this paper, we prove that the set of messages that collide with any given message under this authentication code contains with high probability a message that has small Hamming distance to any other given message. Based on this fact we present extended MITM attacks against different versions of BB84 QKD protocols using the addressed authentication code; for three protocols we describe every single action taken by the adversary. For all protocols the adversary can obtain complete knowledge of the key, and for most protocols her success probability in doing so approaches unity.

    Since the attacks work against all authentication methods which allow to calculate colliding messages, the underlying building blocks of the presented attacks expose the potential pitfalls arising as a consequence of non-ITS authentication in QKDpostprocessing. We propose countermeasures, increasing the eavesdroppers demand for computational power, and also prove necessary and sufficient conditions for upgrading the discussed authentication code to the ITS level.

  • 10. Schumm, T.
    et al.
    Krueger, P.
    Hofferberth, S.
    Lesanovsky, I.
    Wildermuth, S.
    Groth, S.
    Bar-Joseph, I.
    Andersson, L. Mauritz
    Schmiedmayer, J.
    A double well interferometer on an atom chip2006In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 5, no 6, p. 537-558Article in journal (Refereed)
    Abstract [en]

    Radio-Frequency coupling between magnetically trapped atomic states allows to create versatile adiabatic dressed state potentials for neutral atom manipulation. Most notably, a single magnetic trap can be split into a double well by controlling amplitude and frequency of an oscillating magnetic field. We use this to build an integrated matter wave interferometer on an atom chip. Transverse splitting of quasi one-dimensional Bose-Einstein condensates over a wide range from 3 to 80 mu m is demonstrated, accessing the tunnelling regime as well as completely isolated sites. By recombining the two split BECs in time of flight expansion, we realize a matter wave interferometer. The observed interference pattern exhibits a stable relative phase of the two condensates, clearly indicating a coherent splitting process. Furthermore, we measure and control the deterministic phase evolution throughout the splitting process. RF induced potentials are especially suited for integrated micro manipulation of neutral atoms on atom chips: designing appropriate wire patterns enables control over the created potentials to the (nanometer) precision of the fabrication process. Additionally, hight local RF amplitudes can be obtained with only moderate currents. This new technique can be directly implemented in many existing atom chip experiments.

  • 11.
    Sezer, Hasan Cavit
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system2012In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 11, no 6, p. 1685-1694Article in journal (Refereed)
    Abstract [en]

    In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary matrix from the using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation.

  • 12.
    Sjöqvist, Erik
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
    Azimi Mousolou, Vahid
    Department of Mathematics, Faculty of Science, Univ. of Isfahan, Iran.
    Canali, Carlo M.
    School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
    Conceptual aspects of geometric quantum computation2016In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 15, no 10, p. 3995-4011Article in journal (Refereed)
    Abstract [en]

    Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates, and find an explicit physical example where the two types of gates coincide. We identify differencies and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases. 

  • 13.
    Sjöqvist, Erik
    et al.
    Uppsala University.
    Mousolou, Vahid Azimi
    Univ Isfahan, Iran.
    Canali, Carlo M.
    Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
    Conceptual aspects of geometric quantum computation2016In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 15, no 10, p. 3995-4011Article in journal (Refereed)
    Abstract [en]

    Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.

  • 14.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    The multifarious quantum information2006In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 5, no 6, p. 481-502Article in journal (Refereed)
    Abstract [en]

    This paper considers the scope and possibilities of quantum information within the consensus interpretation of the theory. It is pointed out that a prepared quantum state offers a multitude of answers determined by the query directed to it. It predicts the outcome of measurements of alternative observations or allows the performance of a selection of quantum information processes. Knowing the state does not determine which observables can be assigned values, but defining a point of view of the observer allows him to derive outcomes of measurements. However, all predictions are in the form of statistical distributions or correlations between observations. Thus they are intrinsically independent of separations in space and time: like all statistical knowledge they have to be reassessed when new infomation imposes a new initial state. Many properties determined by quantum observations must be assigned to the results of the measurements and not to the physical system itself. Thus the property of nonlocality is a consequence of the probabilistic interpretation only, and it corresponds to no feature assigned to the physical reality.

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