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Articles 1 - 30 of 31
Full-Text Articles in Physical Sciences and Mathematics
Action Principle For Continuous Quantum Measurement, A. Chantasri, Justin Dressel, Andrew N. Jordan
Action Principle For Continuous Quantum Measurement, A. Chantasri, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
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 …
Photon Counting Compressive Depth Mapping, Gregory A. Howland, Daniel J. Lum, Matthew R. Ware, John C. Howell
Photon Counting Compressive Depth Mapping, Gregory A. Howland, Daniel J. Lum, Matthew R. Ware, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We demonstrate a compressed sensing, photon counting lidar system based on the single-pixel camera. Our technique recovers both depth and intensity maps from a single under-sampled set of incoherent, linear projections of a scene of interest at ultra-low light levels around 0.5 picowatts. Only two-dimensional reconstructions are required to image a three-dimensional scene. We demonstrate intensity imaging and depth mapping at 256 × 256 pixel transverse resolution with acquisition times as short as 3 seconds. We also show novelty filtering, reconstructing only the difference between two instances of a scene. Finally, we acquire 32 × 32 pixel real-time video for …
Technical Advantages For Weak-Value Amplification: When Less Is More, Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell
Technical Advantages For Weak-Value Amplification: When Less Is More, Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the …
Strengthening Weak-Value Amplification With Recycled Photons, Justin Dressel, Kevin Lyons, Andrew N. Jordan, Trent M. Graham, Paul G. Kwiat
Strengthening Weak-Value Amplification With Recycled Photons, Justin Dressel, Kevin Lyons, Andrew N. Jordan, Trent M. Graham, Paul G. Kwiat
Mathematics, Physics, and Computer Science Faculty Articles and Research
We consider the use of cyclic weak measurements to improve the sensitivity of weak-value amplification precision measurement schemes. Previous weak-value experiments have used only a small fraction of events, while discarding the rest through the process of “postselection.” We extend this idea by considering recycling of events which are typically unused in a weak measurement. Here we treat a sequence of polarized laser pulses effectively trapped inside an interferometer using a Pockels cell and polarization optics. In principle, all photons can be postselected, which will improve the measurement sensitivity. We first provide a qualitative argument for the expected improvements from …
Quantum Instruments As A Foundation For Both States And Observables, Justin Dressel, Andrew N. Jordan
Quantum Instruments As A Foundation For Both States And Observables, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded, perspective from which to understand the elements of the traditional approach.We first show that in principle all measurable probabilities and correlations can be expressed entirely in terms of quantum instruments without the need for conventional quantum states or observables. We then show how these states and observables reappear as derived quantities by conditioning joint detection probabilities on the first or last measurement in a sequence as a preparation or a …
Weak-Values Technique For Velocity Measurements, Gerardo I. Viza, Julián Martínez-Rincón, Gregory A. Howland, Hadas Frostig, Itay Shomroni, Barak Dayan, John C. Howell
Weak-Values Technique For Velocity Measurements, Gerardo I. Viza, Julián Martínez-Rincón, Gregory A. Howland, Hadas Frostig, Itay Shomroni, Barak Dayan, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a recent Letter, Brunner and Simon proposed an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [Phys. Rev. Lett 105, 010405 (2010)]. Here we demonstrate an interferometric scheme combined with a time-domain analysis to measure longitudinal velocities. The technique employs the near-destructive interference of non-Fourier limited pulses, one Doppler shifted due to a moving mirror in a Michelson interferometer. We achieve a velocity measurement of 400 fm/s and show our estimator to be efficient by reaching its Cramér–Rao bound.
Einstein-Podolsky-Rosen Steering Inequalities From Entropic Uncertainty Relations, James Schneeloch, Curtis J. Broadbent, Stephen P. Walborn, Eric G. Cavalcanti, John C. Howell
Einstein-Podolsky-Rosen Steering Inequalities From Entropic Uncertainty Relations, James Schneeloch, Curtis J. Broadbent, Stephen P. Walborn, Eric G. Cavalcanti, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We use entropic uncertainty relations to formulate inequalities that witness Einstein-Podolsky-Rosen (EPR)-steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the differing natures of the correlations captured by one-way and symmetric steering inequalities and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator-valued measures, and we also derive hybrid steering inequalities between alternate degrees of freedom.
Null Values And Quantum State Discrimination, Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, Curtis J. Broadbent, John C. Howell, Yuval Gefen
Null Values And Quantum State Discrimination, Oded Zilberberg, Alessandro Romito, David J. Starling, Gregory A. Howland, Curtis J. Broadbent, John C. Howell, Yuval Gefen
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.
Rapidly Reconfigurable Optically Induced Photonic Crystals In Hot Rubidium Vapor, Bethany Little, David J. Starling, John C. Howell, Raphael D. Cohen, David Shwa, Nadav Katz
Rapidly Reconfigurable Optically Induced Photonic Crystals In Hot Rubidium Vapor, Bethany Little, David J. Starling, John C. Howell, Raphael D. Cohen, David Shwa, Nadav Katz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission, and diffraction of light. The modulation is achieved through the use of the ac Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling.
Violation Of Continuous-Variable Einstein-Podolsky-Rosen Steering With Discrete Measurements, James Schneeloch, P. Ben Dixon, Gregory A. Howland, Curtis J. Broadbent, John C. Howell
Violation Of Continuous-Variable Einstein-Podolsky-Rosen Steering With Discrete Measurements, James Schneeloch, P. Ben Dixon, Gregory A. Howland, Curtis J. Broadbent, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this Letter, we derive an entropic Einstein-Podolsky-Rosen (EPR) steering inequality for continuous-variable systems using only experimentally measured discrete probability distributions and details of the measurement apparatus. We use this inequality to witness EPR steering between the positions and momenta of photon pairs generated in spontaneous parametric down-conversion. We examine the asymmetry between parties in this inequality, and show that this asymmetry can be used to reduce the technical requirements of experimental setups intended to demonstrate the EPR paradox. Furthermore, we develop a more stringent steering inequality that is symmetric between parties, and use it to show that the down-converted …
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Non-Commutative Stochastic Distributions And Applications To Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.
Residuated Frames With Applications To Decidability, Nikolaos Galatos, Peter Jipsen
Residuated Frames With Applications To Decidability, Nikolaos Galatos, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination, the finite model property and the finite embeddability property, which imply the decidability of the equational/universal theories of the associated residuated lattice-ordered groupoids. In particular these techniques allow us to prove that the variety of involutive FL-algebras and several related varieties have the finite model property.
Long-Term (1951-2007) Rainfall Trends Around Six Indian Cities: Current State, Meteorological, And Urban Dynamics, Shailesh Kumar Kharol, D. G. Kaskaoutis, Anu Rani Sharma, Ramesh P. Singh
Long-Term (1951-2007) Rainfall Trends Around Six Indian Cities: Current State, Meteorological, And Urban Dynamics, Shailesh Kumar Kharol, D. G. Kaskaoutis, Anu Rani Sharma, Ramesh P. Singh
Mathematics, Physics, and Computer Science Faculty Articles and Research
The present study focuses on analyzing the precipitation trends over six Indian cities during the summer monsoon (June-September) covering the period 1951-2007 and also attempting to investigate possible urban forcing and dynamics by examining the variation in precipitation in the upwind and downwind directions. The analysis shows negative trends in the total number of rainy days over Hyderabad (-10.4%), Kanpur (-7.1%), Jaipur (-10.5%), and Nagpur (-4.8%) and positive trends over Delhi (7.4%) and Bangalore (22.9%). On the other hand, decreases of -21.3%, -5.9%, -14.2%, and -14.6% in seasonal rainfall are found over Delhi, Hyderabad, Jaipur, and Kanpur, respectively, whereas Bangalore …
Multi Geophysical Parameters For Earthquake Forecasting, Ramesh P. Singh
Multi Geophysical Parameters For Earthquake Forecasting, Ramesh P. Singh
Mathematics, Physics, and Computer Science Faculty Articles and Research
This article focuses on the importance of keeping the public aware of earthquake forecasting. This article also encourages proper seismic codes to design buildings in the seismic-prone regions because such practice can save lives and property associated with an earthquake.
Practical Approach To Cosmological Perturbations In Modified Gravity, Alessandra Silvestri, Levon Pogosian, Roman V. Buniy
Practical Approach To Cosmological Perturbations In Modified Gravity, Alessandra Silvestri, Levon Pogosian, Roman V. Buniy
Mathematics, Physics, and Computer Science Faculty Articles and Research
The next generation of large scale surveys will not only measure cosmological parameters within the framework of general relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations, departures from the growth in the standard cosmological model can be quantified in terms of two functions of time and Fourier number k. We argue that in local theories of gravity, in the quasistatic approximation, these functions must be ratios of polynomials in k, with the numerator of one function being equal to the denominator of the other. Moreover, the polynomials are even and …
The Classical Limit Of Quantum Optics: Not What It Seems At First Sight, Yakir Aharonov, Alonso Botero, Shmuel Nussinov, Sandu Popescu, Jeff Tollaksen, Lev Vaidman
The Classical Limit Of Quantum Optics: Not What It Seems At First Sight, Yakir Aharonov, Alonso Botero, Shmuel Nussinov, Sandu Popescu, Jeff Tollaksen, Lev Vaidman
Mathematics, Physics, and Computer Science Faculty Articles and Research
What light is and how to describe it has always been a central subject in physics. As our understanding has increased, so have our theories changed: geometrical optics, wave optics and quantum optics are increasingly sophisticated descriptions, each referring to a larger class of phenomena than its predecessor. But how exactly are these theories related? How and when wave optics reduces to geometric optics is a rather simple problem. Similarly, how quantum optics reduces to wave optics has also been considered to be a very simple business. It is not so. As we show here the classical limit of quantum …
Quantum Cheshire Cats, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, Paul Skrzypczyk
Quantum Cheshire Cats, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich, Paul Skrzypczyk
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we present a quantum Cheshire Cat. In a pre- and post-selected experiment we find the Cat in one place, and its grin in another. The Cat is a photon, while the grin is its circular polarization.
Inter- And Intra-Annual Variability Of Vegetation In The Northern Hemisphere And Its Association With Precursory Meteorological Factors, Boksoon Myoung, Yong-Sang Choi, Seungbum Hong, Seon Ki Park
Inter- And Intra-Annual Variability Of Vegetation In The Northern Hemisphere And Its Association With Precursory Meteorological Factors, Boksoon Myoung, Yong-Sang Choi, Seungbum Hong, Seon Ki Park
Mathematics, Physics, and Computer Science Faculty Articles and Research
Determination of phenological variation is one of the most critical challenges in dynamic vegetation modeling, given the lack of a strong theoretical framework. Previous studies generally focused on the timing of a phenological event (e.g., bud-burst or onset of growing season) and its atmospheric prompts, but not on the interactive variations across phenological stages. This study, therefore, investigated the inter- and intra-annual variability existing in all the phenological stages and the relations of the variability with four meteorological variables (surface temperature (Ts), shortwave radiation (SW ), vapor pressure deficit (VPD), and precipitation (PRCP)) using a 25-year (1982-2006) dataset of leaf …
Relation Algebras As Expanded Fl-Algebras, Nikolaos Galatos, Peter Jipsen
Relation Algebras As Expanded Fl-Algebras, Nikolaos Galatos, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
This paper studies generalizations of relation algebras to residuated lattices with a unary De Morgan operation. Several new examples of such algebras are presented, and it is shown that many basic results on relation algebras hold in this wider setting. The variety qRA of quasi relation algebras is defined and shown to be a conservative expansion of involutive FL-algebras. Our main result is that equations in qRA and several of its subvarieties can be decided by a Gentzen system, and that these varieties are generated by their finite members.
Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz
Convex Cones Of Generalized Positive Rational Functions And Nevanlinna-Pick Interpolation, Daniel Alpay, Izchak Lewkowicz
Mathematics, Physics, and Computer Science Faculty Articles and Research
Scalar rational functions with a non-negative real part on the right half plane, called positive, are classical in the study of electrical networks, dissipative systems, Nevanlinna-Pick interpolation and other areas. We here study generalized positive functions, i.e with a non-negative real part on the imaginary axis. These functions form a Convex Invertible Cone, cic in short, and we explore two partitionings of this set: (i) into (infinitely many non-invertible) convex cones of functions with prescribed poles and zeroes in the right half plane and (ii) each generalized positive function can be written as a sum of even and odd parts. …
Topological Convolution Algebras, Daniel Alpay, Guy Salomon
Topological Convolution Algebras, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we introduce a new family of topological convolution algebras of the form ⋃p∈NL2(S,μp), where S is a Borel semi-group in a locally compact group G, which carries an inequality of the type ∥f∗g∥p≤Ap,q∥f∥q∥g∥p for p>q+d where d pre-assigned, and Ap,q is a constant. We give a sufficient condition on the measures μp for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Representation Formulas For Hardy Space Functions Through The Cuntz Relations And New Interpolation Problems, Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Marziano
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce connections between the Cuntz relations and the Hardy space H2 of the open unit disk D. We then use them to solve a new kind of multipoint interpolation problem in H2, where for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves.
Pontryagin De Branges-Rovnyak Spaces Of Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Pontryagin De Branges-Rovnyak Spaces Of Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions which are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper we focus on the case of Hilbert spaces, and introduce in particular a version of the Hardy space. Then we define Blaschke factors and Blaschke products and we consider an interpolation problem. In the second part of the paper we turn to the case of Pontryagin spaces. We first prove some results from the theory of Pontryagin spaces in the quaternionic setting and, in particular, …
Towards A Formulation Of Quantum Theory As A Causally Neutral Theory Of Bayesian Inference, Matthew S. Leifer, Robert W. Spekkens
Towards A Formulation Of Quantum Theory As A Causally Neutral Theory Of Bayesian Inference, Matthew S. Leifer, Robert W. Spekkens
Mathematics, Physics, and Computer Science Faculty Articles and Research
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas themanner in which inferences aremade in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of …
Maximally Epistemic Interpretations Of The Quantum State And Contextuality, Matthew S. Leifer, O. J. E. Maroney
Maximally Epistemic Interpretations Of The Quantum State And Contextuality, Matthew S. Leifer, O. J. E. Maroney
Mathematics, Physics, and Computer Science Faculty Articles and Research
We examine the relationship between quantum contextuality (in both the standard Kochen-Specker sense and in the generalized sense proposed by Spekkens) and models of quantum theory in which the quantum state is maximally epistemic.We find that preparation noncontextual models must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual. This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models. The implication from preparation noncontextual to maximally epistemic then also yields a proof of Bell’s theorem from an Einstein-Podolsky-Rosen-like argument.
Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman
Point–Counterpoint: Can Anything Be Learned From Surveys On The Interpretations Of Quantum Mechanics?, Matthew S. Leifer, Nathan Harshman
Mathematics, Physics, and Computer Science Faculty Articles and Research
"In what follows, Matt Leifer and Nathan Harshman present opposing views on the value of surveys on foundational attitudes towards quantum mechanics. Three such surveys were recently published and their results are summarized in Table 1. Matt takes the `point,’ arguing that such surveys are not useful, while Nathan takes the `counterpoint.’ A complete set of references for both is given at the end."
Annual Patterns Of Atmospheric Pollutions And Episodes Over Cairo Egypt, Y. Aboel Fetouh, Hesham El-Askary, Mohamed El Raey, Mohamed Allali, W. A. Sprigg, Menas Kafatos
Annual Patterns Of Atmospheric Pollutions And Episodes Over Cairo Egypt, Y. Aboel Fetouh, Hesham El-Askary, Mohamed El Raey, Mohamed Allali, W. A. Sprigg, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
The Nile Delta major cities, particularly Cairo, experienced stagnant air pollution episodes, known as Black Cloud, every year over the past decade during autumn. Low-elevated thermal inversion layers play a crucial role in intensifying pollution impacts. Carbon monoxide, ozone, atmospheric temperature, water vapor, and methane measurements from the tropospheric emission spectrometer (TES) on board the Aura have been used to assess the dominant component below the inversion layer. In this study, time series analysis, autocorrelations, and cross correlations are performed to gain a better understanding of the connections between those parameters and their local effect. Satellite-based data were obtained for …
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes, Daniel Alpay, Alon Kipnis
A Generalized White Noise Space Approach To Stochastic Integration For A Class Of Gaussian Stationary Increment Processes, Daniel Alpay, Alon Kipnis
Mathematics, Physics, and Computer Science Faculty Articles and Research
Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.
On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok
On Discrete Analytic Functions: Products, Rational Functions, And Reproducing Kernels, Daniel Alpay, Palle Jorgensen, Ron Seager, Dan Volok
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the Cauchy-Kovalevskaya product of hyperholomorphic functions, and allows us to define rational discrete analytic functions. To define the second product we need a new space of entire functions which is contractively included in the Fock space. We study in this space some counterparts of Schur analysis.
Review Of Computing With Quantum Cats: From Colossus To Qubits And Schrödinger’S Killer App: Race To Build The World’S First Quantum Computer, Matthew S. Leifer
Review Of Computing With Quantum Cats: From Colossus To Qubits And Schrödinger’S Killer App: Race To Build The World’S First Quantum Computer, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
Book reviews of Computing With Quantum Cats: From Colossus To Qubits by John Gribbin and Schrödinger’s Killer App: Race To Build The World’s First Quantum Computer by John Dowling.