575 research outputs found

    Robust and efficient generator of almost maximal multipartite entanglement

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    Quantum chaotic maps can efficiently generate pseudo-random states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the system. We show that such multipartite entanglement is robust, in the sense that, when realistic noise is considered, distillable entanglement of bipartitions remains almost maximal up to a noise strength that drops only polynomially with the number of qubits.Comment: 4 pages, 4 figures. Published versio

    Classical versus quantum errors in quantum computation of dynamical systems

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    We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first kind of errors has a classical limit, the second one has no classical analogue. It is shown that, whereas in the first case (``classical errors'') the decay of fidelity is very sensitive to the dynamical regime, in the second case (``quantum errors'') it is almost independent of the dynamical behavior of the simulated system. Therefore, the rich variety of behaviors found in the study of the stability of quantum motion under ``classical'' perturbations has no correspondence in the fidelity of quantum computation under its natural perturbations. In particular, in this latter case it is not possible to recover the semiclassical regime in which the fidelity decays with a rate given by the classical Lyapunov exponent.Comment: 8 pages, 7 figure

    Entanglement, randomness and chaos

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    Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in various quantum information protocols. The preparation of a random state or, equivalently, the implementation of a random unitary operator, requires a number of elementary one- and two-qubit gates that is exponential in the number n_q of qubits, thus becoming rapidly unfeasible when increasing n_q. On the other hand, pseudo-random states approximating to the desired accuracy the entanglement properties of true random states may be generated efficiently, that is, polynomially in n_q. In particular, quantum chaotic maps are efficient generators of multipartite entanglement among the qubits, close to that expected for random states. This review discusses several aspects of the relationship between entanglement, randomness and chaos. In particular, I will focus on the following items: (i) the robustness of the entanglement generated by quantum chaotic maps when taking into account the unavoidable noise sources affecting a quantum computer; (ii) the detection of the entanglement of high-dimensional (mixtures of) random states, an issue also related to the question of the emergence of classicality in coarse grained quantum chaotic dynamics; (iii) the decoherence induced by the coupling of a system to a chaotic environment, that is, by the entanglement established between the system and the environment.Comment: Review paper, 40 pages, 7 figures, added reference

    A 'User-Friendly' Approach to the Dynamical Equations of Non-Holonomic Systems

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    Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied to linear as well as to non-linear constraints. Only the basic notions of vector calculus on Euclidean 3-space and on tangent bundles are needed. Elementary examples are illustrated.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

    An Error Model for the Cirac-Zoller CNOT gate

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    In the framework of ion-trap quantum computing, we develop a characterization of experimentally realistic imperfections which may affect the Cirac-Zoller implementation of the CNOT gate. The CNOT operation is performed by applying a protocol of five laser pulses of appropriate frequency and polarization. The laser-pulse protocol exploits auxiliary levels, and its imperfect implementation leads to unitary as well as non-unitary errors affecting the CNOT operation. We provide a characterization of such imperfections, which are physically realistic and have never been considered before to the best of our knowledge. Our characterization shows that imperfect laser pulses unavoidably cause a leak of information from the states which alone should be transformed by the ideal gate, into the ancillary states exploited by the experimental implementation.Comment: 10 pages, 1 figure. Accepted as a contributed oral communication in the QuantumComm 2009 International Conference on Quantum Communication and Quantum Networking, Vico Equense, Italy, October 26-30, 200

    Computing the distance between quantum channels: Usefulness of the Fano representation

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    The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.Comment: 8 pages, 7 figure

    How complex is the quantum motion?

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    In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. Here we introduce a notion of complexity for a quantum system and relate it to its stability and reversibility properties.Comment: 4 pages, 3 figures, new figure adde

    Quantum Poincare' recurrences in microwave ionization of Rydberg atoms

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    We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field. The quantum survival probability follows the classical one up to the Heisenberg time and then decays inversely proportional to time, due to tunneling and localization effects. We provide parameter values which should allow one to observe such decay in laboratory experiments. Relations to the 1/f1/f noise are also discussed.Comment: 6 pages, 3 figures, Contribution to the Proceedings of the Conference "Atoms, molecules and quantum dots in laser fields: fundamental processes", Pisa, June 200
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