A probabilistic and information theoretic interpretation of quantum evolutions

In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature and one can measure `which unitary' happened. Likewise, one can give an information-theoretic interpretation to evolutions by defining the entropy of a completely positive map. This entropy gives the rate at which the informational content of the evolution can be compressed. One cannot compress this information and still have the evolution act on an unknown state, but we demonstrate a general scheme to do so probabilistically. This allows one to generalize super-dense coding to the sending of quantum information. One can also define the ``interaction-entanglement'' of a unitary, and concentrate this entanglement.Comment: 9 page

(Quantumness in the context of) Resource Theories

We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be created under the class of operations), and those which are a resource (because they cannot be). One can quantify the worth of the resource by the relative entropy distance to the set of free states, and under certain conditions, this is a unique measure which quantifies the rate of state to state transitions. The framework includes entanglement, asymmetry and purity theory. It also includes thermodynamics, which is a hybrid resource theory combining purity theory and asymmetry. Another hybrid resource theory which merges purity theory and entanglement can be used to study quantumness of correlations and discord, and we present quantumness in this more general framework of resource theories.Comment: review articl

Supernarrow spectral peaks near a kinetic phase transition in a driven, nonlinear micromechanical oscillator

We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving frequency. White noise is injected into the excitation, allowing the system to overcome the activation barrier and switch between the two states. While the oscillator predominately resides in one of the two states for most excitation frequencies, a narrow range of frequencies exist where the occupations of the two states are approximately equal. At these frequencies, the oscillator undergoes a kinetic phase transition that resembles the phase transition of thermal equilibrium systems. We observe a supernarrow peak in the power spectral densities of fluctuations of the oscillator. This peak is centered at the excitation frequency and arises as a result of noise-induced transitions between the two dynamical states.Comment: 4 pages, 4 figure

Can the frequency-dependent specific heat be measured by thermal effusion methods?

It has recently been shown that plane-plate heat effusion methods devised for wide-frequency specific-heat spectroscopy do not give the isobaric specific heat, but rather the so-called longitudinal specific heat. Here it is shown that heat effusion in a spherical symmetric geometry also involves the longitudinal specific heat.Comment: Paper presented at the Fifth International Workshop on Complex Systems (Sendai, September, 2007), to appear in AIP Conference Proceeding

Classical information deficit and monotonicity on local operations

We investigate classical information deficit: a candidate for measure of classical correlations emerging from thermodynamical approach initiated in [Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of information that can be concentrated by use of LOCC and the information contained in subsystems. We show nonintuitive fact, that one way version of this quantity can increase under local operation, hence it does not possess property required for a good measure of classical correlations. Recently it was shown by Igor Devetak, that regularised version of this quantity is monotonic under LO. In this context, our result implies that regularization plays a role of "monotoniser".Comment: 6 pages, revte

Spectral Simplicity of Apparent Complexity, Part II: Exact Complexities and Complexity Spectra

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainty, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. An appendix presents spectral decomposition calculations for one example in full detail.Comment: 27 pages, 12 figures, 2 tables; most recent version at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt2.ht

Effects of electrojet turbulence on a magnetosphere-ionosphere simulation of a geomagnetic storm

Ionospheric conductance plays an important role in regulating the response of the magnetosphere‐ionosphere system to solar wind driving. Typically, models of magnetosphere‐ionosphere coupling include changes to ionospheric conductance driven by extreme ultraviolet ionization and electron precipitation. This paper shows that effects driven by the Farley‐Buneman instability can also create significant enhancements in the ionospheric conductance, with substantial impacts on geospace. We have implemented a method of including electrojet turbulence (ET) effects into the ionospheric conductance model utilized within geospace simulations. Our particular implementation is tested with simulations of the Lyon‐Fedder‐Mobarry global magnetosphere model coupled with the Rice Convection Model of the inner magnetosphere. We examine the impact of including ET‐modified conductances in a case study of the geomagnetic storm of 17 March 2013. Simulations with ET show a 13% reduction in the cross polar cap potential at the beginning of the storm and up to 20% increases in the Pedersen and Hall conductance. These simulation results show better agreement with Defense Meteorological Satellite Program observations, including capturing features of subauroral polarization streams. The field‐aligned current (FAC) patterns show little differences during the peak of storm and agree well with Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) reconstructions. Typically, the simulated FAC densities are stronger and at slightly higher latitudes than shown by AMPERE. The inner magnetospheric pressures derived from Tsyganenko‐Sitnov empirical magnetic field model show that the inclusion of the ET effects increases the peak pressure and brings the results into better agreement with the empirical model.This material is based upon work supported by NASA grants NNX14AI13G, NNX13AF92G, and NNX16AB80G. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work used the XSEDE and TACC computational facilities, supported by National Science Foundation grant ACI-1053575. We would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. We thank the AMPERE team and the AMPERE Science Center for providing the Iridium derived data products. All model output, simulation codes, and analysis routines are being preserved on the NCAR High-Performance Storage System and will be made available upon written request to the lead author of this publication. (NNX14AI13G - NASA; NNX13AF92G - NASA; NNX16AB80G - NASA; National Science Foundation; ACI-1053575 - National Science Foundation

Measurement of Time-of-Arrival in Quantum Mechanics

It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.Comment: References added. To appear in Phys. Rev.