Error probability analysis in quantum tomography: a tool for evaluating experiments

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography. We verify that the error probability can decrease at most exponentially in the number of trials, derive the explicit rate that bounds this decrease, and show that a maximum likelihood estimator achieves this bound. We also show that the statistical notion of identifiability coincides with the tomographic notion of informational completeness. Our result implies that two quantum tomographic apparatuses that have the same risk function, (e.g. variance), can have different error probability, and we give an example in one qubit state tomography. Thus by combining these two approaches we can evaluate, in a reconstruction independent way, the performance of such experiments more discerningly.Comment: 14pages, 2 figures (an analysis of an example is added, and the proof of Lemma 2 is corrected

Electronic 4-wheel drive control device

The internal rotation torque generated during operation of a 4-wheel drive vehicle is reduced using a control device whose clutch is attached to one part of the rear-wheel drive shaft. One torque sensor senses the drive torque associated with the rear wheel drive shaft. A second sensor senses the drive torque associated with the front wheel drive shaft. Revolution count sensors sense the revolutions of each drive shaft. By means of a microcomputer, the engagement of the clutch is changed to insure that the ratio of the torque sensors remains constant

Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the estimation errors and those predicted by an asymptotic analysis. The origin of this discrepancy is the existence of the boundary in the state space imposed by the requirement that density matrices be nonnegative (positive semidefinite). We derive an explicit form of a function reproducing the behavior of the estimation errors with high accuracy by introducing two approximations: a Gaussian approximation of the multinomial distributions of outcomes, and linearizing the boundary. This function gives us an intuition for the behavior of the expected losses for finite data sets. We show that this function can be used to determine the amount of data necessary for the estimation to be treated reliably with the asymptotic theory. We give an explicit expression for this amount, which exhibits strong sensitivity to the true quantum state as well as the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous version, and some typos are correcte

Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A-optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.Comment: 15 pages, 7 figure

The Correlation of Spectral Lag Evolution with Prompt Optical Emission in GRB 080319B

We report on observations of correlated behavior between the prompt gamma-ray and optical emission from GRB 080319B, which confirm that (i) they occurred within the same astrophysical source region and (ii) their respective radiation mechanisms were dynamically coupled. Our results, based upon a new CCF methodology for determining the time-resolved spectral lag, are summarized as follows. First, the evolution in the arrival offset of prompt gamma-ray photon counts between Swift-BAT 15-25 keV and 50-100 keV energy bands (intrinsic gamma-ray spectral lag) appears to be anti-correlated with the arrival offset between prompt 15-350 keV gamma-rays and the optical emission observed by TORTORA (extrinsic optical/gamma-ray spectral lag), thus effectively partitioning the burst into two main episodes at ~T+28+/-2 sec. Second, the rise and decline of prompt optical emission at ~T+10+/-1 sec and ~T+50+/-1 sec, respectively, both coincide with discontinuities in the hard to soft evolution of the photon index for a power law fit to 15-150 keV Swift-BAT data at ~T+8+/-2 sec and ~T+48+/-1 sec. These spectral energy changes also coincide with intervals whose time-resolved spectral lag values are consistent with zero, at ~T+12+/-2 sec and ~T+50+/-2 sec. These results, which are robust across heuristic permutations of Swift-BAT energy channels and varying temporal bin resolution, have also been corroborated via independent analysis of Konus-Wind data. This potential discovery may provide the first observational evidence for an implicit connection between spectral lags and GRB emission mechanisms in the context of canonical fireball phenomenology. Future work includes exploring a subset of bursts with prompt optical emission to probe the unique or ubiquitous nature of this result.Comment: 6 pages, 3 figures. Contributed to the Proceedings of the Sixth Huntsville GRB Symposium. Edited by C.A. Meegan, N. Gehrels, and C. Kouvelioto

Variational Calculation of the Effective Action

An indication of spontaneous symmetry breaking is found in the two-dimensional $\lambda\phi^4$ model, where attention is paid to the functional form of an effective action. An effective energy, which is an effective action for a static field, is obtained as a functional of the classical field from the ground state of the hamiltonian $H[J]$ interacting with a constant external field. The energy and wavefunction of the ground state are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under antiperiodic boundary conditions. A field configuration that is physically meaningful is found as a solution of the quantum mechanical Euler-Lagrange equation in the $J\to 0$ limit. It is shown that there exists a nonzero field configuration in the broken phase of $Z_2$ symmetry because of a boundary effect.Comment: 26 pages, REVTeX, 7 postscript figures, typos corrected and two references adde