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

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

Action principle for continuous quantum measurement

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most-likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.Comment: Published version. 8 pages, 3 figures, movies available at http://youtu.be/OQ3PwkSKEUw and http://youtu.be/sTlV2amQtj

Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements

We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multi-particle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semi-weak polarization measurement based on Fresnel reflection. We also point out a non- trivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.Comment: 4 pages, 6 figure

Accuracy and Racial Biases of Recidivism Prediction Instruments

Algorithms have recently become prevalent in the criminal justice system. Tools known as recidivism prediction instruments (RPIs) are being used all over the country to assess the likelihood that a criminal defendant will reoffend at some point in the future. In June of 2016, researchers at ProPublica published an analysis claiming an RPI called COMPAS was biased against black defendants. This claim sparked a nation-wide debate as to how fairness of an algorithm should be measured, and exposed the many ways that algorithms are not necessarily fair. Algorithms are used in the criminal justice system because they are regarded as more accurate and less biased than human predictions; however, there does not exist a contemporary comparison of the performance of human and algorithmic recidivism predictions. To address this, we set out to determine if COMPAS is more accurate than human prediction, and to identify how the racial biases of human recidivism predictions compare to the racial biases of the COMPAS algorithm. After establishing a baseline performance of human prediction, we explore whether incorporating human judgment into algorithms can enhance prediction accuracy

Non-Fermi liquid behavior in nearly charge ordered layered metals

Non-Fermi liquid behavior is shown to occur in two-dimensional metals which are close to a charge ordering transition driven by the Coulomb repulsion. A linear temperature dependence of the scattering rate together with an increase of the electron effective mass occur above T*, a temperature scale much smaller than the Fermi temperature. It is shown that the anomalous temperature dependence of the optical conductivity of the quasi-two-dimensional organic metal alpha-(BEDT-TTF)2MHg(SCN)4, with M=NH4 and Rb, above T*=50-100 K, agrees qualitatively with our predictions for the electronic properties of nearly charge ordered two-dimensional metals.Comment: accepted in Phys. Rev. Let

Electronic properties of correlated metals in the vicinity of a charge order transition: optical spectroscopy of α\alpha-(BEDT-TTF)2M_2MHg(SCN)4_4 (MM = NH4_4, Rb, Tl)

The infrared spectra of the quasi-two-dimensional organic conductors $\alpha$-(BEDT-TTF)$_2$$M$Hg(SCN)$_4$ ($M$ = NH$_4$, Rb, Tl) were measured in the range from 50 to 7000 \cm down to low temperatures in order to explore the influence of electronic correlations in quarter-filled metals. The interpretation of electronic spectra was confirmed by measurements of pressure dependant reflectance of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ at T=300 K. The signatures of charge order fluctuations become more pronounced when going from the NH$_4$ salt to Rb and further to Tl compounds. On reducing the temperature, the metallic character of the optical response in the NH$_4$ and Rb salts increases, and the effective mass diminishes. For the Tl compound, clear signatures of charge order are found albeit the metallic properties still dominate. From the temperature dependence of the electronic scattering rate the crossover temperature is estimated below which the coherent charge-carriers response sets in. The observations are in excellent agreement with recent theoretical predictions for a quarter-filled metallic system close to charge order

Evidence for a Bulk Complex Order-Parameter in Y0.9Ca0.1Ba2Cu3O7-delta Thin Films

We have measured the penetration depth of overdoped Y0.9Ca0.1Ba2Cu3O7-delta (Ca-YBCO) thin films using two different methods. The change of the penetration depth as a function of temperature has been measured using the parallel plate resonator (PPR), while its absolute value was obtained from a quasi-optical transmission measurements. Both sets of measurements are compatible with an order parameter of the form: Delta*dx2-y2+i*delta*dxy, with Delta=14.5 +- 1.5 meV and delta=1.8 meV, indicating a finite gap at low temperature. Below 15 K the drop of the scattering rate of uncondensed carriers becomes steeper in contrast to a flattening observed for optimally doped YBCO films. This decrease supports our results on the penetration depth temperature dependence. The findings are in agreement with tunneling measurements on similar Ca-YBCO thin films.Comment: 11 pages, 4 figure