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

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

Violating the Modified Helstrom Bound with Nonprojective Measurements

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and non-guess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.Comment: 5 pages, 2 figure

Implementing generalized measurements with superconducting qubits

We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. First, we consider two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup, or using an indirect ancilla qubit measurement. Second, we decompose an arbitrary purity-preserving two-outcome measurement into single qubit unitary rotations and a partial projection. Third, we systematically reduce any multiple-outcome measurement to a sequence of such two-outcome measurements and unitary operations. Finally, we consider how to define suitable fidelity measures for multiple-outcome generalized measurements.Comment: 13 pages, 3 figure

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

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

Optical properties of the iron-pnictide analog BaMn2As2

We have investigated the infrared and Raman optical properties of BaMn2As2 in the ab-plane and along the c-axis. The most prominent features in the infrared spectra are the Eu and A2u phonon modes which show clear TO-LO splitting from the energy loss function analysis. All the phonon features we observed in infrared and Raman spectra are consistent with the calculated values. Compared to the iron-pnictide analog AFe2As2, this compound is much more two-dimensional in its electronic properties. For E || c-axis, the overall infrared reflectivity is insulating like. Within the ab-plane the material exhibits a semiconducting behavior. An energy gap 2{\Delta}=48 meV can be clearly identified below room temperature.Comment: 5 pages, 7 figure