Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance

We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations relies on an implicit assumption that is generally incompatible with the Bell-Kochen-Specker-Spekkens contextuality theorems, and which results in averaging the deviations over a non-positive-semidefinite joint quasiprobability distribution. For unbiased measurements, the error admits a concrete interpretation as the dispersion in the estimation of the mean induced by the measurement ambiguity. We demonstrate how to directly measure not only this dispersion but also every observable moment with the same experimental data, and thus demonstrate that perfect distributional estimations can have nonzero error according to this measure. We conclude that the inequalities using these definitions do not capture the spirit of Heisenberg's eponymous inequality, but do indicate a qualitatively different relationship between dispersion and disturbance that is appropriate for ensembles being probed by all outcomes of an apparatus. To reconnect with the discussion of Heisenberg, we suggest alternative definitions of error and disturbance that are intrinsic to a single apparatus outcome. These definitions naturally involve the retrodictive and interdictive states for that outcome, and produce complementarity and error-disturbance inequalities that have the same form as the traditional Heisenberg relation.Comment: 15 pages, 8 figures, published versio

Microspectroscopy and Imaging in the THz Range Using Coherent CW Radiation

A novel THz near-field spectrometer is presented which allows to perform biological and medical studies with high spectral resolution combined with a spatial resolution down to l/100. In the setup an aperture much smaller than the used wavelength is placed in the beam very close to the sample. The sample is probed by the evanescent wave behind the aperture. The distance is measured extremely accurate by a confocal microscope. We use monochromatic sources which provide powerful coherent cw radiation tuneable from 50 GHz up to 1.5 THz. Transmission and reflection experiments can be performed which enable us to study solids and molecules in aqueous solution. Examples for spectroscopic investigations on biological tissues are presented.Comment: 4 pages, 5 figures, email: [email protected]

Sufficient conditions for uniqueness of the weak value

We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel J, Agarwal S and Jordan A N 2010 Phys. Rev. Lett. 104, 240401. We also respond to criticism of our work in [arXiv:1105.4188v1] concerning a proposed counter-example to the uniqueness of the definition of the generalized weak value. The counter-example does not satisfy our prescription in the case of an underspecified measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the measurement emerges and the unique definition in the weak limit holds. We also prove a theorem regarding the uniqueness of the definition under our sufficient conditions for the general case. Finally, a second proposed counter-example in [arXiv:1105.4188v6] is shown not to satisfy the sufficiency conditions for the provided theorem.Comment: 17 pages, final published respons

Microwave inductance of thin metal strips

We have measured the frequency-dependent, complex impedance of thin metal strips in a broad range of microwave frequencies (45~MHz to 20~GHz). The spectra are in good agreement with theoretical predictions of an RCL model. The resistance, inductance, and capacitance, which govern the microwave response, depend on the strip width and thickness as well as on the strip and substrate materials. While the strip resistance scales inversely with the cross section, the inductance depends on the width of the strip, but not on the thickness (in the limit of small thickness).Comment: 3 pages, 2 figure

Past observable dynamics of a continuously monitored qubit

Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.Comment: 11 pages, 4 figure

DC and high-frequency conductivity of the organic metals beta"-(BEDT-TTF)2SF5RSO3 (R = CH2CF2 and CHF)

The temperature dependences of the electric-transport properties of the two-dimensional organic conductors beta"-(BEDT-TTF)2SF5CH2CF2SO3, beta"-(d8-BEDT-TTF)2SF5CH2CF2SO3, and beta"-(BEDT-TTF)2SF5CHFSO3 are measured by dc methods in and perpendicular to the highly-conducting plane. Microwave measurements are performed at 24 and 33.5 GHz to probe the high-frequency behavior from room temperature down to 2 K. Superconductivity is observed in beta"-(BEDT-TTF)2SF5CH2CF2SO3 and its deuterated analogue. Although all the compounds remain metallic down to low-temperatures, they are close to a charge-order transition. This leads to deviations from a simple Drude behavior of the optical conductivity which become obvious already in the microwave range. In beta"-(BEDT-TTF)2SF5CH2CF2SO3, for instance, charge fluctuations cause an increase in microwave resistivity for T < 20 K which is not detected in dc measurements. beta"-(BEDT-TTF)2SF5CHFSO3 exhibits a simple metallic behavior at all frequencies. In the dc transport, however, we observe indications of localization in the perpendicular direction.Comment: 8 pages, 9 figure

Using poststratification to improve abundance estimates from multispecies surveys: a study of juvenile flatfishes

Population assessments seldom incorporate habitat information or use previously observed distributions of fish density. Because habitat affects the spatial distribution of fish density and overall abundance, the use of habitat information and previous estimates of fish density can produce more precise and less biased population estimates. In this study, we describe how poststratification can be applied as an unbiased estimator to data sets that were collected under a probability sampling design, typical of many multispecies trawl surveys. With data from a multispecies survey of juvenile flatfish, we show how poststratification can be applied to a data set that was not collected under a probability sampling design, where both the precision and the bias are unknown. For each of four species, three estimates of total abundance were compared: 1) unstratified; 2) poststratified by habitat; and 3) poststratified by habitat and fish density (high fish density and low fish density) in nearby years. Poststratification by habitat gave more precise and (or) less design-biased estimates than an unstratified estimator for all species in all years. Poststratification by habitat and fish density produced the most precise and representative estimates when the sample size in the high fish-density and low fish-density strata were sufficient (in this study, n≥20 in the high fish-density stratum, n≥9 in the low fish-density stratum). Because of the complexities of statistically testing the annual stratified data, we compared three indices of abundance for determining statistically significant changes in annual abundance. Each of the indices closely approximated the annual differences of the poststratified estimates. Selection of the most appropriate index was dependent upon the species’ density distribution within habitat and the sample size in the different habitat areas. The methods used in this study are particularly useful for estimating individual species abundance from multispecies surveys and for retrospective s