A5058743784- Quantum Mechanics and Applications
- Quantum Information and Cryptography
- Quantum Computing Algorithms and Architecture
- Quantum many-body systems
- Quantum and electron transport phenomena
- Advanced Thermodynamics and Statistical Mechanics
- Advanced Operator Algebra Research
- Quantum-Dot Cellular Automata
- Cold Atom Physics and Bose-Einstein Condensates
- Cellular Automata and Applications
- Spectral Theory in Mathematical Physics
- Statistical Mechanics and Entropy
- Mathematical Analysis and Transform Methods
- Noncommutative and Quantum Gravity Theories
- Scientific Measurement and Uncertainty Evaluation
- Philosophy and History of Science
- Advanced Topics in Algebra
- Topological Materials and Phenomena
- Quantum chaos and dynamical systems
- Radioactive Decay and Measurement Techniques
- Holomorphic and Operator Theory
- Quantum Mechanics and Non-Hermitian Physics
- Random Matrices and Applications
- Algebraic structures and combinatorial models
- Computability, Logic, AI Algorithms
Leibniz University Hannover
2015-2024
University of Copenhagen
2019
Leibniz University of Applied Sciences
2014-2018
Leibniz Association
2016
University of Illinois Urbana-Champaign
2011
Research Institute for Philosophy Hannover
2010
Technische Universität Braunschweig
2001-2010
Bulgarian Academy of Sciences
2010
Institute for Nuclear Research and Nuclear Energy
2010
Universität Innsbruck
2005
We present a measure of entanglement that can be computed effectively for any mixed state an arbitrary bipartite system. show it does not increase under local manipulations the system, and use to obtain bound on teleportation capacity distillable states.
A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations product states, and Einstein-Podolsky-Rosen otherwise. Any modeled hidden-variable theory hence satisfies all generalized Bell's inequalities. It shown an explicit example that the converse this statement false.
We show how to compute or at least estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, entanglement-assisted classical capacity, one-shot and a quantity involving transpose operation, shown be general upper bound on quantum even allowing finite errors. All bounds explicitly evaluated case of one-mode channel with attenuation amplification noise.
We construct a unique optimal quantum device for turning finite number of $d$-level systems in the same unknown pure state \ensuremath{\sigma} into $M$ kind, an approximation $M$-fold tensor product \ensuremath{\sigma}.
We construct a set of ${2}^{{2}^{n}}$ independent Bell-correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that are satisfied if and only correlations considered allow local classical model. All these can be summarized single, albeit nonlinear inequality. show quantum satisfy this condition provided state has positive partial transpose respect to any grouping n into subsystems. also provide an efficient algorithm finding maximal...
We show how to simplify the computation of entanglement formation and relative entropy for states, which are invariant under a group local symmetries. For several examples groups we characterize state spaces, these groups. specific calculate measures. In particular, derive an explicit formula $(U\ensuremath{\bigotimes}U)$-invariant find counterexample additivity conjecture entanglement.
We discuss the entanglement properties of bipartite states with Gaussian Wigner functions. For separability, and positivity partial transpose, we establish explicit necessary sufficient criteria in terms covariance matrix state. It is shown that, for systems composed a single oscillator Alice an arbitrary number Bob, transpose implies separability. However, this implication fails two oscillators on each side, as show by constructing five parameter family bound entangled states.
We study the entanglement properties of a closed chain harmonic oscillators that are coupled via translationally invariant Hamiltonian, where coupling acts only on position operators. consider ground state and thermal states this system, which Gaussian states. The these can be completely characterized analytically when one uses logarithmic negativity as measure entanglement.
We provide a security analysis for continuous variable quantum key distribution protocols based on the transmission of two-mode squeezed vacuum states measured via homodyne detection. employ version entropic uncertainty relation smooth entropies to give lower bound number secret bits which can be extracted from finite runs protocol. This is valid under general coherent attacks, and gives rise keys are composably secure. For comparison, we also assumption collective attacks. both scenarios,...
Secret communication over public channels is one of the central pillars a modern information society. Using quantum key distribution this achieved without relying on hardness mathematical problems which might be compromised by improved algorithms or future computers. State-of-the-art requires composable security against coherent attacks for finite number distributed states as well robustness implementation side-channels. Here, we present an continuous-variable satisfying these requirements....
While the slogan "no measurement without disturbance" has established itself under name of Heisenberg effect in consciousness scientifically interested public, a precise statement this fundamental feature quantum world remained elusive, and serious attempts at rigorous formulations it as consequence theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities...
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here we resolve the conflict by way of an analysis possible conceptualizations measurement error and disturbance in quantum mechanics. We discuss two approaches to adapting classic notion root-mean-square measurements. One is based on concept noise operator; its natural operational content that mean deviation values observables measured jointly, thus applicability limited cases where such joint...
We present a construction for quantum error correcting codes. The basic ingredients are graph and finite Abelian group, from which the code can explicitly be obtained. prove necessary sufficient conditions such that resulting corrects certain number of errors. This allows simple verification one-error property codes length 5 in any dimension. As examples, we construct large class maximum distance separable codes, i.e. saturating Singleton bound, as well 10 detecting three
We show that for a fixed amount of entanglement, two-mode squeezed states are those maximize Einstein-Podolsky-Rosen-like correlations. use this fact to determine the entanglement formation all symmetric Gaussian corresponding two modes. This is first instance in which measure has been determined genuine continuous variable systems.
We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding (3) orthonormal bases of maximally entangled vectors, (4) unitary operators with respect to the Hilbert–Schmidt scalar product and (5) depolarizing operations, whose Kraus can be chosen unitary. The schemes are assumed `tight' in sense that all Hilbert spaces involved have same finite dimension d, classical channel distinguishes d 2 signals. A general construction procedure for unitaries,...
We present a general model for quantum channels with memory and show that it is sufficiently to encompass all causal automata: any process in which outputs up some time $t$ do not depend on inputs at times ${t}^{\ensuremath{'}}>t$ can be decomposed into concatenated channel. then examine different physical setups may operated the transfer of (private) classical information. These include either receiver or malicious third party have control initializing memory. introduce channel...
Quantum information processing is usually associated with a specific computational basis. Nevertheless, for deeper understanding of the fundamental principles quantum computing, it essential to investigate what fidelity universal operations that are basis independent; i.e., task perform optimally operation on qubit or register in an unknown state. In this paper we introduce universal-NOT gate takes as input arbitrary state $|\ensuremath{\Psi}〉$ and generates output close possible orthogonal...
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on mathematical side, communication aspects physical side. Known results families of generalized are summarized. investigate maximal violations as well states not violating (certain) inequalities. Finally, we relation between inequality entanglement properties currently discussed in quantum information theory.
Bell’s inequalities are briefly presented in the context of order-unit spaces and then studied some detail framework C*-algebras. The discussion is specialized to quantum field theory. Maximal Bell correlations β(φ,𝒜(𝒪1), 𝒜(𝒪2)) for two subsystems localized regions 𝒪1 𝒪2 constituting a system state φ defined, along with concept maximal violations. After study these ideas general, properties vacuum states arbitrary models studied. For example, it shown that decay exponentially product lowest...
We introduce a Gaussian version of the entanglement formation adapted to bipartite states by considering decompositions into pure only. show that this quantity is an monotone under operations and provide simplified computation for arbitrary many modes. For case one mode per site remaining variational problem can be solved analytically. If considered state in addition symmetric with respect interchanging two modes, we prove additivity measure. Moreover, only single copy, our measure coincides...
We present a method to estimate entanglement measures in experiments. show how lower bound on generic measure can be derived from the measured expectation values of any finite collection witnesses. Hence witness measurements are given quantitative meaning without need further experimental data. apply our results recent multiphoton experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving bounds formation and geometric this experiment.