141,744 research outputs found

    Experimentally realizable control fields in quantum Lyapunov control

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    As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system's instantaneous message in the control loop. Often, the Lyapunov control is confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time-delay on the Lyapunov control, and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the controlled system. These results suggest that the Lyapunov control is robust gainst time delay, easy to realize and effective for high-dimensional quantum systems

    The isomorphism conjecture for solvable groups in Waldhausen’s A-theory

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    On the finiteness of the classifying space for the family of virtually cyclic subgroups

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    Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups

    Asymptotic Behavior of Error Exponents in the Wideband Regime

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    In this paper, we complement Verd\'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of Rz(0)R_z(0) and Rz˙(0)\dot{R_z}(0) are calculated, where Rz(1/B)R_z(1/B) is the maximum rate at which information can be transmitted over a channel with bandwidth B/2B/2 when the error-exponent is constrained to be greater than or equal to z.z. Based on this calculation, we say that a sequence of input distributions is near optimal if both Rz(0)R_z(0) and Rz˙(0)\dot{R_z}(0) are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver.Comment: 59 pages, 6 figure
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