Michael R. Frey

A gamma-based framework for modeling variable-rate MPEG video sources: the GOP GBAR model

A flexible model called the group-of-pictures gamma-beta auto-regression (GOP GBAR) model based on gamma-distributed variables is proposed for variable-rate MPEG video sources. This model is an extension of Heymans (see IEEE/ACM Trans. Networking, vol.5, p.554-60, 1997) GBAR model for video teleconferencing. The GOP GBAR model explicitly accounts for MPEG GOP cyclicity and has convenient analytical properties with easily estimated parameters. Possible extensions of the GOP GBAR model are proposed to capture special features of MPEG video.

Spectral Nulling on Transmit via Nonlinear FM Radar Waveforms

Modern radars operate in electromagnetic environments crowded with other RF users. Adaptive spectral nulling on transmit can reduce interference from and to these other RF users. An analytical theory is developed for spectral nulling by a minimal adjustment, or offset, to the phase of the radar pulse that maintains constant pulse amplitude. Numerical examples show that a small time-varying phase offset designed by the proposed method can produce deep spectral nulls at one or more chosen frequencies in the radars spectral sidelobes with little other effect on the pulse spectrum or ambiguity function.

Wavelength conversion and call connection probability in WDM networks

Call connection probability in an all-optical network using wavelength division multiplexing (WDM) depends on the number of WDM wavelengths and on the network capability for wavelength conversion at network nodes. New closed-form expressions for call connection probability are derived which reflect these dependencies. These expressions are combined in a converter availability model to study the impact of wavelength conversion on call connection probability and the tradeoff between network wavelength conversion capability and the number of WDM wavelengths.

Quantum speed limits--primer, perspectives, and potential future directions

Fundamental physical limits on the speed of state evolution in quantum systems exist in the form of the Mandelstam–Tamm and the Margolus–Levitin inequalities. We give an expository review of the development of these quantum speed limit (QSL) inequalities, including extensions to different energy statistics and generalizations to mixed system states and open and multipartite systems. The QSLs expressed by these various inequalities have implications for quantum computation, quantum metrology, and control of quantum systems. These connections are surveyed, and some important open questions are noted.

Probing the qudit depolarizing channel

For the quantum depolarizing channel with any finite dimension, we compare three schemes for channel identification: unentangled probes, probes maximally entangled with an external ancilla, and maximally entangled probe pairs. This comparison includes cases where the ancilla is itself depolarizing and where the probe is circulated back through the channel before measurement. Compared on the basis of (quantum Fisher) information gained per channel use, we find broadly that entanglement with an ancilla dominates the other two schemes, but only if entanglement is cheap relative to the cost per channel use and only if the external ancilla is well shielded from depolarization. We arrive at these results by a relatively simple analytical means. A separate, more complicated analysis for partially entangled probes shows for the qudit depolarizing channel that any amount of probe entanglement is advantageous and that the greatest advantage comes with maximal entanglement.

A Wiener filter, state-space flux-optimal control against escape from a potential well

Escape from a potential well, often identified with system failure, is reformulated for a class of two-dimensional dynamical systems as exiting the safe region of the system state space bounded by the separatrix derived from the potential well. A control against system failure based on minimizing the state-space flux out of this safe region is considered. For systems subject to weak external forcing with available control power exceeding a certain threshold, the finite lag, state-space flux-optimal control against failure, is shown to involve a Wiener filter. A non-Wiener solution is proposed for available power below this threshold. These results hold for wide-sense stationary forcing with any statistics and any spectrum.

The Pitman Closeness of a Class of Scaled Estimators

Abstract Scaling is known to reduce the mean square error of unbiased estimators of the mean. Pitman closeness, like mean square error, is often used as a criterion for comparing competing estimators. Scaling is reexamined from the perspective of Pitman closeness. Scaling is found to offer not only reduced mean square error, but also, in many cases, an advantage in terms of Pitman closeness. However, these advantages accrue to a substantial degree only in experiments with low signal-to-noise ratio and very costly measurements.

Score operators of a qubit with applications

The score operators of a quantum system are the symmetric logarithmic derivatives of the system’s parametrically defined quantum state. Score operators are central to the calculation of the quantum Fisher information (QFI) associated with the state of the system, and the QFI determines the maximum precision with which the state parameters can be estimated. We give a simple, explicit expression for score operators of a qubit and apply this expression in a series of settings. We treat in detail the task of identifying a quantum Pauli channel from the state of its qubit output, and we show that a “balanced” probe state is highly robust for this purpose. The QFI for this task is a matrix, and we study its determinant, for which we establish a Cramér-Rao inequality.

Measurement of a subsystem of a coupled quantum system

The Stern-Gerlach (SG) apparatus for measuring the spin of an uncharged spin-1/2 particle is the archetypal quantum sensing device. We study this device for the new problem of measuring the spin of a particle that is coupled externally to another particle. Specifically, we treat two coupled particles in which a single particle is measured by the SG device while the other is not. We show simulations of how the binding energy associated with the external coupling is completely converted to potential energy and kinetic energy as the single particle separates spatially within the magnetic field of the SG device. Additionally we show simulations of how the initial particle acceleration within the SG devices relates to the coupling, the quantum state of the two-particle system, and the initial spatial dispersion of the particle within the SG device. The results of our analysis, though obtained specifically for the SG apparatus, may be generic to other quantum measurement devices with similar external coupling.

An analytic theory for power law detection of bursty targets in multiplicative noise

A detection problem is formulated for a bursty target in multiplicative noise. A power law detector is considered for this problem, with the detector exponent matched to the burstiness of the target. A simple analytic theory is related for the detector exponent: a theory applicable, in particular, to the family of gamma-Weibull multiplicative noise models.