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Articles 1 - 30 of 31
Full-Text Articles in Physical Sciences and Mathematics
Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan
Weak Values Are Universal In Von Neumann Measurements, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for …
Efficient High-Dimensional Entanglement Imaging With A Compressive-Sensing Double-Pixel Camera, Gregory A. Howland, John C. Howell
Efficient High-Dimensional Entanglement Imaging With A Compressive-Sensing Double-Pixel Camera, Gregory A. Howland, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We implement a double-pixel compressive-sensing camera to efficiently characterize, at high resolution, the spatially entangled fields that are produced by spontaneous parametric down-conversion. This technique leverages sparsity in spatial correlations between entangled photons to improve acquisition times over raster scanning by a scaling factor up to n2/log(n) for n-dimensional images. We image at resolutions up to 1024 dimensions per detector and demonstrate a channel capacity of 8.4 bits per photon. By comparing the entangled photons’ classical mutual information in conjugate bases, we violate an entropic Einstein-Podolsky-Rosen separability criterion for all measured resolutions. More broadly, our result indicates that …
Double Lorentzian Atomic Prism, David J. Starling, Steven M. Bloch, Praveen K. Vudyasetu, Joseph S. Choi, Bethany Little, John C. Howell
Double Lorentzian Atomic Prism, David J. Starling, Steven M. Bloch, Praveen K. Vudyasetu, Joseph S. Choi, Bethany Little, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present an atomic prism spectrometer that utilizes the steep linear dispersion between two strongly absorbing hyperfine resonances of rubidium. We resolve spectral lines 50 MHz apart and, utilizing a larger part of the available spectrum than only between the two resonances, we spatially separate collinear pump, signal, and idler beams resulting from a four-wave mixing process. Due to the high transparency possible between the resonances, these results have applications in the filtering of narrow-band entangled photons and interaction-free measurements.
Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell
Quantum Mutual Information Capacity For High-Dimensional Entangled States, P. Ben Dixon, Gregory A. Howland, James Schneeloch, John C. Howell
Mathematics, Physics, and Computer Science Faculty Articles and Research
High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.
Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan
Contextual-Value Approach To The Generalized Measurement Of Observables, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We present a detailed motivation for and definition of the contextual values of an observable, which were introduced by Dressel et al. [Phys. Rev. Lett. 104, 240401 (2011)]. The theory of contextual values is a principled approach to the generalized measurement of observables. It extends the well-established theory of generalized statemeasurements by bridging the gap between partial state collapse and the observables that represent physically relevant information about the system. To emphasize the general utility of the concept, we first construct the full theory of contextual values within an operational formulation of classical probability theory, paying special attention to observable …
Significance Of The Imaginary Part Of The Weak Value, Justin Dressel, Andrew N. Jordan
Significance Of The Imaginary Part Of The Weak Value, Justin Dressel, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
Unlike the real part of the generalized weak value of an observable, which can in a restricted sense be operationally interpreted as an idealized conditioned average of that observable in the limit of zero measurement disturbance, the imaginary part of the generalized weak value does not provide information pertaining to the observable being measured.What it does provide is direct information about howthe initial statewould be unitarily disturbed by the observable operator. Specifically, we provide an operational interpretation for the imaginary part of the generalized weak value as the logarithmic directional derivative of the postselection probability along the unitary flow generated …
Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers, Justin Dressel, Y. Choi, Andrew N. Jordan
Measuring Which-Path Information With Coupled Electronic Mach-Zehnder Interferometers, Justin Dressel, Y. Choi, Andrew N. Jordan
Mathematics, Physics, and Computer Science Faculty Articles and Research
We theoretically investigate a generalized “which-path” measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wavelike behavior to optimally …
Pbr, Epr, And All That Jazz, Matthew S. Leifer
Pbr, Epr, And All That Jazz, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. …
Variability And Trends Of Aerosol Properties Over Kanpur, Northern India Using Aeronet Data (2001–10), Dimitris G. Kaskaoutis, Ramesh P. Singh, Ritesh Gautam, Manish Sharma, P. G. Kosmopoulos, S. N. Tripathi
Variability And Trends Of Aerosol Properties Over Kanpur, Northern India Using Aeronet Data (2001–10), Dimitris G. Kaskaoutis, Ramesh P. Singh, Ritesh Gautam, Manish Sharma, P. G. Kosmopoulos, S. N. Tripathi
Mathematics, Physics, and Computer Science Faculty Articles and Research
Natural and anthropogenic aerosols over northern India play an important role in influencing the regional radiation budget, causing climate implications to the overall hydrological cycle of South Asia. In the context of regional climate change and air quality, we discuss aerosol loading variability and trends at Kanpur AERONET station located in the central part of the Indo-Gangetic plains (IGP), during the last decade (2001-10). Ground-based radiometric measurements show an overall increase in column-integrated aerosol optical depth (AOD) on a yearly basis. This upward trend is mainly due to a sustained increase in the seasonal/monthly averaged AOD during the winter (Dec-Feb) …
Fog- And Cloud-Induced Aerosol Modification Observed By The Aerosol Robotic Network (Aeronet), T. F. Eck, B. N. Holben, J. S. Reid, D. M. Giles, M. A. Rivas, Ramesh P. Singh, S. N. Tripathi, C. J. Bruegge, S. Platnick, G. T. Arnold, N. A. Krotkov, S. A. Carn, A. Sinyuk, O. Dubovik, A. Arola, J. S. Schafer, P. Artaxo, A. Smirnov, H. Chen, P. Goloub
Fog- And Cloud-Induced Aerosol Modification Observed By The Aerosol Robotic Network (Aeronet), T. F. Eck, B. N. Holben, J. S. Reid, D. M. Giles, M. A. Rivas, Ramesh P. Singh, S. N. Tripathi, C. J. Bruegge, S. Platnick, G. T. Arnold, N. A. Krotkov, S. A. Carn, A. Sinyuk, O. Dubovik, A. Arola, J. S. Schafer, P. Artaxo, A. Smirnov, H. Chen, P. Goloub
Mathematics, Physics, and Computer Science Faculty Articles and Research
Large fine mode-dominated aerosols (submicron radius) in size distributions retrieved from the Aerosol Robotic Network (AERONET) have been observed after fog or low-altitude cloud dissipation events. These column-integrated size distributions have been obtained at several sites in many regions of the world, typically after evaporation of low-altitude cloud such as stratocumulus or fog. Retrievals with cloud-processed aerosol are sometimes bimodal in the accumulation mode with the larger-size mode often similar to 0.4-0.5 mu m radius (volume distribution); the smaller mode, typically similar to 0.12 to similar to 0.20 mu m, may be interstitial aerosol that were not modified by incorporation …
Influence Of Anomalous Dry Conditions On Aerosols Over India: Transport, Distribution And Properties, Dimitris G. Kaskaoutis, Ritesh Gautam, Ramesh P. Singh, E. E. Housos, D. Goto, S. Singh, A. Bartzokas, P. G. Kosmopoulos, Manish Sharma, N. C. Hsu, B. N. Holben, T. Takemura
Influence Of Anomalous Dry Conditions On Aerosols Over India: Transport, Distribution And Properties, Dimitris G. Kaskaoutis, Ritesh Gautam, Ramesh P. Singh, E. E. Housos, D. Goto, S. Singh, A. Bartzokas, P. G. Kosmopoulos, Manish Sharma, N. C. Hsu, B. N. Holben, T. Takemura
Mathematics, Physics, and Computer Science Faculty Articles and Research
A synergy of satellite and ground-based radiometric observations, along with chemical transport modeling, was used for the assessment of the influence of drought monsoon conditions of 2002 and prolonged dry pre-monsoon period of 2003 on aerosol properties over south Asia, with emphasis over northern India. Reanalysis data are also examined for studying the dry anomalous period from the climatological mean, that show prevalence of westerlies under anticyclonic circulation and subsidence favoring the accumulation of aerosols. TRMM observations over south Asia indicate significant rainfall deficit over northwestern India in July 2002 and May-June 2003. Subsequently, the anomalous and prolonged dry conditions …
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
Everything Is Entangled, Roman V. Buniy, Stephen D. H. Hsu
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other - the reduced density matrix describing any pair is likely to be separable.
An Algebraic Classification Of Entangled States, Roman V. Buniy, Thomas W. Kephart
An Algebraic Classification Of Entangled States, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamental sets of classes.
New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart
New Invariants For Entangled States, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured in the literature.
Toward Solving The Cosmological Constant Problem By Embedding, Roman V. Buniy, Thomas W. Kephart
Toward Solving The Cosmological Constant Problem By Embedding, Roman V. Buniy, Thomas W. Kephart
Mathematics, Physics, and Computer Science Faculty Articles and Research
The typical scalar field theory has a cosmological constant problem. We propose a generic mechanism by which this problem is avoided at tree level by embedding the theory into a larger theory. The metric and the scalar field coupling constants in the original theory do not need to be fine-tuned, while the extra scalar field parameters and the metric associated with the extended theory are fine-tuned dynamically. Hence, no fine-tuning of parameters in the full Lagrangian is needed for the vacuum energy in the new physical system to vanish at tree level. The cosmological constant problem can be solved if …
Impact Of Vegetation On Land-Atmosphere Coupling Strength And Its Implication For Desertification Mitigation Over East Asia, Boksoon Myoung, Yong-Sang Choi, Suk-Jin Choi, Seon Ki Park
Impact Of Vegetation On Land-Atmosphere Coupling Strength And Its Implication For Desertification Mitigation Over East Asia, Boksoon Myoung, Yong-Sang Choi, Suk-Jin Choi, Seon Ki Park
Mathematics, Physics, and Computer Science Faculty Articles and Research
Desertification of the East Asian drylands and the consequent dust transport have been serious concerns for adjacent Asian countries as well as the western United States. Tree planting has been considered one applicable strategy to mitigate the desertification. However, the desired effect of the tree planting would not be brought to fruition unless the newly planted trees change the coupling characteristics between the land and the atmosphere. Based on this perception, we attempt to clarify the effects of vegetation on the coupling strength between the atmosphere and land surface, and we suggest the most efficient areas of tree planting for …
White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony
White Noise Based Stochastic Calculus Associated With A Class Of Gaussian Processes, Daniel Alpay, Haim Attia, David Levanony
Mathematics, Physics, and Computer Science Faculty Articles and Research
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.
An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia
An Interpolation Problem For Functions With Values In A Commutative Ring, Daniel Alpay, Haim Attia
Mathematics, Physics, and Computer Science Faculty Articles and Research
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization …
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential …
Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen
Stochastic Processes Induced By Singular Operators, Daniel Alpay, Palle Jorgensen
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in …
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …
Entropy And Information Causality In General Probabilistic Theories (Addendum), Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew S. Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce, Robin Wilke
Entropy And Information Causality In General Probabilistic Theories (Addendum), Howard Barnum, Jonathan Barrett, Lisa Orloff Clark, Matthew S. Leifer, Robert Spekkens, Nicholas Stepanik, Alex Wilce, Robin Wilke
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of that paper.
Teleportation In General Probabilistic Theories, Howard Barnum, Jonathan Barrett, Matthew S. Leifer, Alex Wilce
Teleportation In General Probabilistic Theories, Howard Barnum, Jonathan Barrett, Matthew S. Leifer, Alex Wilce
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, do support a teleportation protocol. We isolate a natural class of composite systems that we term regular, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields …
Response To Griffiths, Matthew S. Leifer
Response To Griffiths, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
"First of all, I would like to thank Prof. Griffith for his comments. The exchange has reminded me of the series of letters that appeared in Physics Today following the publication of an article by Chandralekha Singh, Mario Belloni, and Wolfgang Christian on improving the teaching of undergraduate quantum mechanics (see http://ptonline.aip.org/ journals/doc/PHTOAD-ft/vol_60/iss_3/8_1.shtml). In those responses, both Griffiths and Travis Norsen argued that students’ understanding of quantum mechanics would be vastly improved if they were taught more about the foundations of quantum theory, and I wholeheartedly agree with that sentiment. The thing is, Griffiths argued vociferously that this should be …
Review Of Elegance And Enigma: The Quantum Interviews, Matthew S. Leifer
Review Of Elegance And Enigma: The Quantum Interviews, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A review of Elegance and Enigma: The Quantum Interviews, edited by Maximilian Schlosshauer.
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement, Matthew S. Leifer
Review Of The Mathematical Language Of Quantum Theory: From Uncertainty To Entanglement, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
A book review of The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement by Teiko Heinosaari and Mario Ziman.
Synergistic Use Of Remote Sensing And Modeling For Tracing Dust Storms In The Mediterranean, D. G. Kaskaoutis, Anup K. Prasad, P. G. Kosmopoulos, P. R. Sinha, S. K. Kharol, P. Gupta, Hesham El-Askary, Menas Kafatos
Synergistic Use Of Remote Sensing And Modeling For Tracing Dust Storms In The Mediterranean, D. G. Kaskaoutis, Anup K. Prasad, P. G. Kosmopoulos, P. R. Sinha, S. K. Kharol, P. Gupta, Hesham El-Askary, Menas Kafatos
Mathematics, Physics, and Computer Science Faculty Articles and Research
This study focuses on the detection of the dust source region and monitoring of the transport of the dust plume from its primary outflow to final deposition. The application area is the Sahara desert and the eastern Mediterranean, where two dust events occurred during the period 4–6 February 2009, an unusual event for a winter period. The Aqua-MODIS and OMI observations clearly define the spatial distribution of the dust plumes, while the CALIPSO observations of total attenuated backscatter (TAB) at 532 nm, depolarization ratio (DR), and attenuated color ratio (1064/532 nm) on 5 February 2009 provide a clear view and …
The New Publishing Scene And The Tenure Case: An Administrator’S View, Daniele C. Struppa
The New Publishing Scene And The Tenure Case: An Administrator’S View, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
No abstract provided.
Bicomplex Numbers And Their Elementary Functions, M. E. Luna-Elizarrarás, M. Shapiro, Daniele C. Struppa, Adrian Vajiac
Bicomplex Numbers And Their Elementary Functions, M. E. Luna-Elizarrarás, M. Shapiro, Daniele C. Struppa, Adrian Vajiac
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. We describe how to define elementary functions in such an algebra (polynomials, exponential functions, and trigonometric functions) as well as their inverse functions (roots, logarithms, inverse trigonometric functions). Our goal is to show that a function theory on bicomplex numbers is, in some sense, a better generalization of the theory of holomorphic functions of one variable, than the classical theory of holomorphic functions in two complex variables.