Sensing Small Changes in a Wave Chaotic Scattering System

Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ Scattering Fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.Comment: 14 pages, 11 figures, as published on J. Appl. Phy

Information-theoretic limitations on approximate quantum cloning and broadcasting

We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control on the performance of generalized UQCMs on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a-priori information in the context of cloning. For example, we can control the performance of an antisymmetric analogue of the UQCM in recovering from the loss of $n-k$ fermionic particles.Comment: 13 pages; new results on approximate cloning between general subspaces, e.g., cloning of fermion

Sensor Based on Extending the Concept of Fidelity to Classical Waves

We propose and demonstrate a remote sensor scheme by applying the quantum mechanical concept of fidelity loss to classical waves. The sensor makes explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to sensitively and remotely measure the presence of small perturbations. The loss of fidelity is measured through a classical wave-analog of the Loschmidt echo by employing a single-channel time-reversal mirror to rebroadcast a probe signal into the perturbed system. We also introduce the use of exponential amplification of the probe signal to partially overcome the effects of propagation losses and to vary the sensitivity.Comment: 4 pages, 2 figure