Nonclassical Measurement Research Articles

A quantum-information theoretic analysis of three-flavor neutrino oscillations: Quantum entanglement, nonlocal and nonclassical features of neutrinos.

Correlations exhibited by neutrino oscillations are studied via quantum-information theoretic quantities. We show that the strongest type of entanglement, genuine multipartite entanglement, is persistent in the flavor changing states. We prove the existence of Bell-type nonlocal features, in both its absolute and genuine avatars. Finally, we show that a measure of nonclassicality, dissension, which is a generalization of quantum discord to the tripartite case, is nonzero for almost the entire range of time in the evolution of an initial electron-neutrino. Via these quantum-information theoretic quantities, capturing different aspects of quantum correlations, we elucidate the differences between the flavor types, shedding light on the quantum-information theoretic aspects of the weak force.

Cauchy–Schwarz inequality-based criteria for the non-classicality of sub-Poisson and antibunched light

We discuss non-classicality of photon antibunching and sub-Poisson photon statistics. The difference K between the variance and the mean of the particle number operator as a measure of non-classicality of a state is discussed. The non-classicality of quantum states, discussed here, is different from another non-classicality, related with Bell's inequalities and entanglement though both can be traced to the violation of an inequality implied by an assumption of classicality that utilized the Cauchy–Schwarz inequality in the derivation.

Nonclassicality and criticality in symmetry-protected magnetic phases

Quantum and global discord in a spin-1 Heisenberg chain subject to single-ion anisotropy (uniaxial field) are studied using exact diagonalisation and the density matrix renormalisation group (DMRG). We find that these measures of quantum nonclassicality are able to detect the quantum phase transitions confining the symmetry protected Haldane phase and show critical scaling with universal exponents. Moreover, in the case of thermal states, we find that quantum discord can increase with increasing temperature.

Offsetting or Enhancing Behavior: An Empirical Analysis of Motorcycle Helmet Safety Legislation.

This study uses state-level panel data from a 33-year period to test the hypotheses of offsetting and enhancing behavior with regards to motorcycle helmet legislation. Results presented in this article find no evidence of offsetting behavior and are consistent with the presence of enhancing behavior. State motorcycle helmet laws are estimated to reduce motorcycle crashes by 18.4% to 31.9%. In the absence of any behavioral adaptations among motorcyclists mandatory helmet laws are not expected to have any significant impact on motorcycle crash rates. The estimated motorcycle crash reductions do not appear to be driven by omitted variable bias or nonclassical measurement error in reported crashes. Overall, the results strongly suggest that mandatory helmet laws yield significant changes in motorcycle mobility in the form of reduced risk taking and/or decreased utilization.

Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $\ensuremath{\tau}$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP), and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance $D$ for a fixed value of both the depth $\ensuremath{\tau}$ and NP in the whole range $[0,1]$ of their values, as well as the NP for a given value of $\ensuremath{\tau}$ such that $\ensuremath{\tau}>0.315\phantom{\rule{0.16em}{0ex}}4$. Conversely, pure states are the most nonclassical single-qubit states with respect to $\ensuremath{\tau}$ for a given $D$, NP versus $D$, and $\ensuremath{\tau}$ versus NP. We also show the ``relativity'' of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states. This implies an operational interpretation of the nonclassical distance as the potential for the entanglement of formation.

Coherent states for the Kepler–Coulomb problem on a sphere

An algebraic approach to Kepler problem in a curved space is introduced. By using this approach, the creation and annihilation operators associated to this system and their algebra are calculated. These operators satisfy a deformed Weyl–Heisenberg algebra which can be assumed as a deformed su(2) algebra. By using this fact, the nonlinear coherent states of this system are constructed. The scalar product and Bargmann representation of this family of nonlinear coherent states are constructed. The present contribution shows that these nonlinear coherent states possess some non-classical features which strongly depend on the Kepler coupling constant and space curvature. Depending on the non-classical measures, the smaller the curvature parameter, the more the non-classical features. Moreover, the stronger Kepler constant provides more non-classical features.

Language Barriers and Immigrant Health Production

We study the impact of language deficiency on the health production of childhood migrants to Australia. Our identification strategy relies on a quasi-experiment comparing immigrants arriving at different ages and from different linguistic origins by utilising a measure of differences along a continuous range of linguistic distances. Our main results indicate a large negative effect of English deficiency on physical health that is robust to a range of different specifications.In the presence of considerable non-classical measurement error in self-reported language proficiency, our results provide lower and upper bounds for the true effect of English deficiency on health of one half and a full standard deviation in the health score respectively. The empirical analysis is framed in terms of a Grossman model which indicates a twofold role of language skills in health production: language deficiency directly affects the efficiency of health production and indirectly affects access to health inputs. We provide some suggestive evidence on the relative importance of these distinct roles.

Closed-form estimation of nonparametric models with non-classical measurement errors

This paper proposes closed-form estimators for nonparametric regressions using two measurements with non-classical errors. One (administrative) measurement has location-/scale-normalized errors, but the other (survey) measurement has endogenous errors with arbitrary location and scale. For this setting of data combination, we derive closed-form identification of nonparametric regressions, and practical closed-form estimators that perform well with small samples. Applying this method to NHANES III, we study how obesity explains health care usage. Clinical measurements and self reports of BMI are used as two measurements with normalized errors and endogenous errors, respectively. We robustly find that health care usage increases with obesity.

Bias in estimating border- and distance-related trade costs: Insights from an oligopoly model

Regressions of price differences between locations in different countries without controlling for the local market structure and the location of origin will lead to a biased estimate of the impact of national boundaries. We demonstrate that non-classical measurement error in distance and unaccounted mark-up differences across countries are responsible for these biases. In a quantitative exercise based on our previous work (Coşar et al., 2014), we show that the estimated border effect with price difference regressions overstates the true border effect by a factor of two or more.

Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors

This paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes, which is of empirical importance. We show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest, which has been observed in linear parametric models. Two-step consistent estimators of the parameters of interest are proposed. We also show that the proposed estimators are consistent with a rate faster than n−1/4 under a certain metric, and the proposed estimators of the finite-dimensional unknown parameters obtain root-n asymptotic normality. Monte Carlo evidences show that the proposed estimators perform well under a variety of identification conditions. An application to instrumental variables estimation of Engel curves illustrates the usefulness of our method. It supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful Engel curves.

Generation of optical-terahertz biphoton pairs via spontaneous parametric down-conversion

We examine the features of parametric down-conversion for generating non-classical optical-terahertz biphoton fields. The calculations were performed for a second-order correlation function and noise reduction factor (NRF), which were selected as measures of non-classicality of the field states. NRF measurement schemes were found to be less advantageous. Overall system temperature at which non-classical effects are still observable has been estimated as about 10 K. The priority of the main complicating factors for the quantum-optical measurements in the terahertz range has been determined. Thus, the most important parameter is the temperature of the system, after that come the absorption losses at terahertz frequencies, and the parametric conversion efficiency has the lowest impact. Increasing the pump radiation power has been found to be inefficient for "noise" suppression in this case. The calculations performed were based on lithium niobate dispersion properties due to its outstanding nonlinear optical properties and because it is frequently used for optical-to-terahertz frequency conversion.

Discriminating strength: a bona fide measure of non-classical correlations

A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state ρ of a composite system AB as a probe for a quantum illumination task (e.g. see Lloyd 2008 Science 321 1463), in which one is asked to remotely discriminate between the two following scenarios: (i) either nothing happens to the probe, or (ii) the subsystem A is transformed via a local unitary whose properties are partially unspecified when producing ρ. This new measure can be seen as the discrete version of the recently introduced interferometric power measure (Girolami et al 2013 e-print arXiv:1309.1472) and, at least for the case in which A is a qubit, it is shown to coincide (up to an irrelevant scaling factor) with the local quantum uncertainty measure of Girolami, Tufarelli and Adesso (2013 Phys. Rev. Lett. 110 240402). Analytical expressions are derived which allow us to formally prove that, within the set of separable configurations, the maximum value of our non-classicality measure is achieved over the set of quantum-classical states (i.e. states ρ which admit a statistical unravelling where each element of the associated ensemble is distinguishable via local measures on B).

Elementary quantum gates with Gaussian states

We study the question of converting initially Gaussian states into non-Gaussian ones by two- and three-photon subtraction to improve non-classical properties of the conditional optical fields. We show the photon subtraction may effectively generate non-Gaussian states only in case of small values of the mean values of the position and momentum operators. In particular, the photon-subtracted state can be made arbitrary close to Gaussian state in limiting case of large initial amplitude of displacement. Use of initial displacement in input Gaussian states opens wider prospects to manipulate them. In particular, realization of probabilistic Hadamard gate with input Gaussian states is discussed where photon subtraction is motive force able unevenly to increase measure of non-classicality of the output state. Subtraction of larger number of photons enables to increase fidelity and non-classical measure of the conditional states.

Super-resolved phase measurements at the shot noise limit by parity measurement.

Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.

Adding a single photon to a coherent state

We investigate the connection between the particle nature of light and its nonclassical character. When we can associate a precise number of photons, in some sense, to a particular state of light, the state possesses a full particle nature. We show that whenever a complete particle nature emerges in the state of light, the corresponding nonclassical measure becomes unity, and the state becomes maximally nonclassical.

Nonclassical states, measurements, and phenomena of light

On taking a positive operator-valued measure (POVM), we introduce nonclassical measurements, together with nonclassical phenomena, in a manner similar to that applied to nonclassical states. The quantitative measure of nonclassicality for the measurements is also defined, and any projective measurement is shown to be nonclassical. When the regularization process is applied to a projective measurement, it becomes a POVM measurement, and its nonclassical measure decreases to vanish at the end.

Coherent states of composite bosons

We present a systematic analysis of coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator. Depending on the elementary particles comprising the composite particles, we gauge the resemblance between this eigenstate and traditional coherent states through typical measures of nonclassicality, such as quadrature variances and Mandel's $Q$ parameter. Furthermore, we show that the eigenstate of the coboson annihilation operator is useful in estimating the maximum eigenvalue of the coboson number operator.

The consequences of measurement error when estimating the impact of obesity on income

AbstractThis paper examines the consequences of using self-reported measures of BMI when estimating the effect of BMI on income for women using both Irish and US data. We find that self-reported BMI is subject to substantial measurement error and that this error deviates from classical measurement error. These errors cause the traditional least squares estimator to overestimate the relationship between BMI and income. We show that neither the conditional expectation estimator nor the instrumental variables approach adequately address the bias and briefly discuss alternative approaches that could be considered when faced with non-classical measurement error.JEL codesC13, C26, I14

Certified quantum non-demolition measurement of a macroscopic material system

Quantum non-demolition (QND) measurements improve sensitivity by evading measurement back-action. The technique was first proposed to detect mechanical oscillations in gravity wave detectors,and demonstrated in the measurement of optical fields, leading to the development of rigorous criteria to distinguish QND from similar non-classical measurements. Recent QND measurements of macroscopic material systems such as atomic ensembles, and mechanical oscillators, show some QND features, but not full QND character. Here we demonstrate certified QND measurement of the collective spin of an atomic ensemble. We observe quantum state preparation (QSP) and information-damage trade-off (IDT) beyond their classical limits by seven and twelve standard deviations, respectively. Our techniques complement recent work with microscopic systems, and can be used for quantum metrology and memory, the preparation and detection of non-gaussian states, and proposed quantum simulation and information protocols. They should enable QND measurements of dynamical quantum variables and the realization of QND-based quantum information protocols.

Achieving steady-state entanglement of remote micromechanical oscillators by cascaded cavity coupling

In this paper, we propose a scheme for generating steady-state entanglement of remote micromechanical oscillators in unidirectionally-coupled cavities. For the system of two mechanical oscillators, we show that when two cavity modes in each cavity are driven at red- and blue-detuned sidebands, respectively, a stationary two-mode squeezed vacuum state of the two mechanical oscillators can be generated with the help of the cavity dissipation. The degree of squeezing is controllable by adjusting the relative strength of the pump lasers. Our calculations also show that the achieved mechanical entanglement is robust against thermal fluctuations of phononic environments. For the case of multiple mechanical oscillators, we find that the steady-state genuine multipartite entanglement can also be built up among the remote mechanical oscillators by the cavity dissipation. The present scheme does not require nonclassical light input or conditional quantum measurements, and it can be realized with current experimental technology.