Compatibility of quantum states

We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some properties of this measure, and discuss its relation to the problem of combining two observers' states of knowledge.Comment: 4 pages, no figure

TIME-VARIANT SPECTRAL ANALYSIS OF SURFACE EMG SIGNALS – EXEMPLARILY SHOWN FOR ARCHERY

To analyse the spectral density of electromyographic (EMG) signals Fourier transforms are commonly used. The prerequisite of this transform is that the analysed signal is stationary. Generally, this can not be assumed for the electromyograms of muscle contractions of human movement. A new method to analyse non-stationary biological signals is the time-variant spectral analysis. The aim of this paper is to use the timevariant spectral analysis in a realistic sport application to show connections of the athlete’s level and the spectral density of the EMG. Five top-level archers participated in the study. The results suggest, that a higher level of performance generally corresponds to lower median-frequencies and a smaller variability of the median-frequencies of the EMG-signals

Semiclassical properties and chaos degree for the quantum baker's map

We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy

Experimental Polarization State Tomography using Optimal Polarimeters

We report on the experimental implementation of a polarimeter based on a scheme known to be optimal for obtaining the polarization vector of ensembles of spin-1/2 quantum systems, and the alignment procedure for this polarimeter is discussed. We also show how to use this polarimeter to estimate the polarization state for identically prepared ensembles of single photons and photon pairs and extend the method to obtain the density matrix for generic multi-photon states. State reconstruction and performance of the polarimeter is illustrated by actual measurements on identically prepared ensembles of single photons and polarization entangled photon pairs

Hypersensitivity to Perturbations in the Quantum Baker's Map

We analyze a randomly perturbed quantum version of the baker's transformation, a prototype of an area-conserving chaotic map. By numerically simulating the perturbed evolution, we estimate the information needed to follow a perturbed Hilbert-space vector in time. We find that the Landauer erasure cost associated with this information grows very rapidly and becomes much larger than the maximum statistical entropy given by the logarithm of the dimension of Hilbert space. The quantum baker's map thus displays a hypersensitivity to perturbations that is analogous to behavior found earlier in the classical case. This hypersensitivity characterizes ``quantum chaos'' in a way that is directly relevant to statistical physics.Comment: 8 pages, LATEX, 3 Postscript figures appended as uuencoded fil

On kinematics and dynamics of independent pion emission

Multiparticle boson states, proposed recently for 'independently' emitted pions in heavy ion collisions, are reconsidered in standard second quantized formalism and shown to emerge from a simplistic chaotic current dynamics. Compact equations relate the density operator, the generating functional of multiparticle counts, and the correlator of the external current to each other. 'Bose-Einstein-condensation' is related to the external pulse. A quantum master equation is advocated for future Monte-Carlo simulations.Comment: 10 pages LaTeX, Sec.7 adde

Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

Realistic simulations of single-spin nondemolition measurement by magnetic resonance force microscopy

A requirement for many quantum computation schemes is the ability to measure single spins. This paper examines one proposed scheme: magnetic resonance force microscopy, including the effects of thermal noise and back-action from monitoring. We derive a simplified equation using the adiabatic approximation, and produce a stochastic pure state unraveling which is useful for numerical simulations.Comment: 33 pages LaTeX, 9 figure files in EPS format. Submitted to Physical Review

Optimal Quantum Trajectories for Continuous Measurement

We define an ideal optimal quantum measurement as that measurement on the apparatus for which the average algorithmic information in the measurement record is minimized. We apply the definition to a chaotic system subject to continuous (Markov) quantum nondemolition measurements. For optimized measurements the average information in the record is much closer to the von Neumann entropy than in the nonoptimized case, but increases more quickly in the chaotic region than in the regular region