Quantum Information in Time-Frequency Continuous Variables Nicolas Fabre
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Information and Entropy in Quantum Theory
Information and Entropy in Quantum Theory O J E Maroney Ph.D. Thesis Birkbeck College University of London Malet Street London WC1E 7HX arXiv:quant-ph/0411172v1 23 Nov 2004 Abstract Recent developments in quantum computing have revived interest in the notion of information as a foundational principle in physics. It has been suggested that information provides a means of interpreting quantum theory and a means of understanding the role of entropy in thermodynam- ics. The thesis presents a critical examination of these ideas, and contrasts the use of Shannon information with the concept of ’active information’ introduced by Bohm and Hiley. We look at certain thought experiments based upon the ’delayed choice’ and ’quantum eraser’ interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of ’active information’ in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell’s Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. -
Notes on the Theory of Quantum Clock
NOTES ON THE THEORY OF QUANTUM CLOCK I.Tralle1, J.-P. Pellonp¨a¨a2 1Institute of Physics, University of Rzesz´ow,Rzesz´ow,Poland e-mail:[email protected] 2Department of Physics, University of Turku, Turku, Finland e-mail:juhpello@utu.fi (Received 11 March 2005; accepted 21 April 2005) Abstract In this paper we argue that the notion of time, whatever complicated and difficult to define as the philosophical cat- egory, from physicist’s point of view is nothing else but the sum of ’lapses of time’ measured by a proper clock. As far as Quantum Mechanics is concerned, we distinguish a special class of clocks, the ’atomic clocks’. It is because at atomic and subatomic level there is no other possibility to construct a ’unit of time’ or ’instant of time’ as to use the quantum transitions between chosen quantum states of a quantum ob- ject such as atoms, atomic nuclei and so on, to imitate the periodic circular motion of a clock hand over the dial. The clock synchronization problem is also discussed in the paper. We study the problem of defining a time difference observable for two-mode oscillator system. We assume that the time dif- ference obsevable is the difference of two single-mode covariant Concepts of Physics, Vol. II (2005) 113 time observables which are represented as a time shift covari- ant normalized positive operator measures. The difficulty of finding the correct value space and normalization for time dif- ference is discussed. 114 Concepts of Physics, Vol. II (2005) Notes on the Theory of Quantum Clock And the heaven departed as a scroll when it is rolled together;.. -
Engineering Ultrafast Quantum Frequency Conversion
Engineering ultrafast quantum frequency conversion Der Naturwissenschaftlichen Fakultät der Universität Paderborn zur Erlangung des Doktorgrades Dr. rer. nat. vorgelegt von BENJAMIN BRECHT aus Nürnberg To Olga for Love and Support Contents 1 Summary1 2 Zusammenfassung3 3 A brief history of ultrafast quantum optics5 3.1 1900 – 1950 ................................... 5 3.2 1950 – 2000 ................................... 6 3.3 2000 – today .................................. 8 4 Fundamental theory 11 4.1 Waveguides .................................. 11 4.1.1 Waveguide modelling ........................ 12 4.1.2 Spatial mode considerations .................... 14 4.2 Light-matter interaction ........................... 16 4.2.1 Nonlinear polarisation ........................ 16 4.2.2 Three-wave mixing .......................... 17 4.2.3 More on phasematching ...................... 18 4.3 Ultrafast pulses ................................. 21 4.3.1 Time-bandwidth product ...................... 22 4.3.2 Chronocyclic Wigner function ................... 22 4.3.3 Pulse shaping ............................. 25 5 From classical to quantum optics 27 5.1 Speaking quantum .............................. 27 iii 5.1.1 Field quantisation in waveguides ................. 28 5.1.2 Quantum three-wave mixing .................... 30 5.1.3 Time-frequency representation .................. 32 5.1.3.1 Joint spectral amplitude functions ........... 32 5.1.3.2 Schmidt decomposition ................. 35 5.2 Understanding quantum ........................... 36 5.2.1 Parametric -
Notes on the Theory of Quantum Clock
NOTES ON THE THEORY OF QUANTUM CLOCK I.Tralle1, J.-P. Pellonp¨a¨a2 1Institute of Physics, University of Rzesz´ow,Rzesz´ow,Poland e-mail:[email protected] 2Department of Physics, University of Turku, Turku, Finland e-mail:juhpello@utu.fi (Received 11 March 2005; accepted 21 April 2005) Abstract In this paper we argue that the notion of time, whatever complicated and difficult to define as the philosophical cat- egory, from physicist’s point of view is nothing else but the sum of ’lapses of time’ measured by a proper clock. As far as Quantum Mechanics is concerned, we distinguish a special class of clocks, the ’atomic clocks’. It is because at atomic and subatomic level there is no other possibility to construct a ’unit of time’ or ’instant of time’ as to use the quantum transitions between chosen quantum states of a quantum ob- ject such as atoms, atomic nuclei and so on, to imitate the periodic circular motion of a clock hand over the dial. The clock synchronization problem is also discussed in the paper. We study the problem of defining a time difference observable for two-mode oscillator system. We assume that the time dif- ference obsevable is the difference of two single-mode covariant Concepts of Physics, Vol. II (2005) 113 time observables which are represented as a time shift covari- ant normalized positive operator measures. The difficulty of finding the correct value space and normalization for time dif- ference is discussed. 114 Concepts of Physics, Vol. II (2005) Notes on the Theory of Quantum Clock And the heaven departed as a scroll when it is rolled together;.. -
Ballistic Electron Transport in Graphene Nanodevices and Billiards
Ballistic Electron Transport in Graphene Nanodevices and Billiards Dissertation (Cumulative Thesis) for the award of the degree Doctor rerum naturalium of the Georg-August-Universität Göttingen within the doctoral program Physics of Biological and Complex Systems of the Georg-August University School of Science submitted by George Datseris from Athens, Greece Göttingen 2019 Thesis advisory committee Prof. Dr. Theo Geisel Department of Nonlinear Dynamics Max Planck Institute for Dynamics and Self-Organization Prof. Dr. Stephan Herminghaus Department of Dynamics of Complex Fluids Max Planck Institute for Dynamics and Self-Organization Dr. Michael Wilczek Turbulence, Complex Flows & Active Matter Max Planck Institute for Dynamics and Self-Organization Examination board Prof. Dr. Theo Geisel (Reviewer) Department of Nonlinear Dynamics Max Planck Institute for Dynamics and Self-Organization Prof. Dr. Stephan Herminghaus (Second Reviewer) Department of Dynamics of Complex Fluids Max Planck Institute for Dynamics and Self-Organization Dr. Michael Wilczek Turbulence, Complex Flows & Active Matter Max Planck Institute for Dynamics and Self-Organization Prof. Dr. Ulrich Parlitz Biomedical Physics Max Planck Institute for Dynamics and Self-Organization Prof. Dr. Stefan Kehrein Condensed Matter Theory, Physics Department Georg-August-Universität Göttingen Prof. Dr. Jörg Enderlein Biophysics / Complex Systems, Physics Department Georg-August-Universität Göttingen Date of the oral examination: September 13th, 2019 Contents Abstract 3 1 Introduction 5 1.1 Thesis synopsis and outline.............................. 10 2 Fundamental Concepts 13 2.1 Nonlinear dynamics of antidot superlattices..................... 13 2.2 Lyapunov exponents in billiards............................ 20 2.3 Fundamental properties of graphene......................... 22 2.4 Why quantum?..................................... 31 2.5 Transport simulations and scattering wavefunctions................ -
The Boundaries of Nature: Special & General Relativity and Quantum
“The Boundaries of Nature: Special & General Relativity and Quantum Mechanics, A Second Course in Physics” Edwin F. Taylor's acceptance speech for the 1998 Oersted medal presented by the American Association of Physics Teachers, 6 January 1998 Edwin F. Taylor Center for Innovation in Learning, Carnegie Mellon University, Pittsburgh, PA 15213 (Now at 22 Hopkins Road, Arlington, MA 02476-8109, email [email protected] , web http://www.artsaxis.com/eftaylor/ ) ABSTRACT Public hunger for relativity and quantum mechanics is insatiable, and we should use it selectively but shamelessly to attract students, most of whom will not become physics majors, but all of whom can experience "deep physics." Science, engineering, and mathematics students, indeed anyone comfortable with calculus, can now delve deeply into special and general relativity and quantum mechanics. Big chunks of general relativity require only calculus if one starts with the metric describing spacetime around Earth or black hole. Expressions for energy and angular momentum follow, along with orbit predictions for particles and light. Feynman's Sum Over Paths quantum theory simply commands the electron: Explore all paths. Students can model this command with the computer, pointing and clicking to tell the electron which paths to explore; wave functions and bound states arise naturally. A second full year course in physics covering special relativity, general relativity, and quantum mechanics would have wide appeal -- and might also lead to significant advancements in upper-level courses for the physics major. © 1998 American Association of Physics Teachers INTRODUCTION It is easy to feel intimidated by those who have in the past received the Oersted Medal, especially those with whom I have worked closely in the enterprise of physics teaching: Edward M. -
Time and Frequency Division Report
Time and Frequency Division Goal The broad mission of the Time and Frequency Division is to provide official U.S. time and related quantities to support a wide range of uses in industry, national infrastructure, research, and among the general public. DIVISION STRATEGY The division’s research and metrology ac- tivities comprise three vertically integrated components, each of which constitutes a strategic element: 1. Official time: Accurate and precise realization of official U.S. time (UTC) and frequency. 2. Dissemination: A wide range of mea- surement services to efficiently and effectively distribute U.S. time and frequency and related quantities – pri- marily through free broadcast services available to any user 24/7/365. 3. Research: Research and technolo- gy development to improve time and frequency standards and dissemination. Part of this research includes high-impact programs in areas such as quantum information processing, atom-based sensors, and laser development and applications, which evolved directly from research to make better frequency standards (atomic clocks). Overview These three components – official time, dissemination, and research – are closely integrated. For example, all Division dissemination services tie directly to the Division’s realization of official time (UTC), and much of the Division’s research is enabled by the continual availability of precision UTC. Our modern technology and economy depend critically on the broad availability of precision timing, frequency, and synchronization. NIST realization and dissemination of time and frequency – continually improved by NIST research and development – is a crucial part of a series of informal national timing infrastructures that enable such essential technologies as: • Telecommunications and computer networks • Utility distribution • GPS, widely available in every cell phone and smartphone as well as GPS receivers • Electronic financial transactions 1 • National security and intelligence applications • Research Strategic Goal: Official Time Intended Outcome and Background U.S. -
Weierstrass Transform on Howell's Space-A New Theory
IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 16, Issue 6 Ser. IV (Nov. – Dec. 2020), PP 57-62 www.iosrjournals.org Weierstrass Transform on Howell’s Space-A New Theory 1 2* 3 V. N. Mahalle , S.S. Mathurkar , R. D. Taywade 1(Associate Professor, Dept. of Mathematics, Bar. R.D.I.K.N.K.D. College, Badnera Railway (M.S), India.) 2*(Assistant Professor, Dept. of Mathematics, Govt. College of Engineering, Amravati, (M.S), India.) 3(Associate Professor, Dept. of Mathematics, Prof. Ram Meghe Institute of Technology & Research, Badnera, Amravati, (M.S), India.) Abstract: In this paper we have explained a new theory of Weierstrass transform defined on Howell’s space. The definition of the Weierstrass transform on this space of test functions is discussed. Some Fundamental theorems are proved and some results are developed. Weierstrass transform defined on Howell’s space is linear, continuous and one-one mapping from G to G c is also discussed. Key Word: Weierstrass transform, Howell’s Space, Fundamental theorem. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 10-12-2020 Date of Acceptance: 25-12-2020 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction A new theory of Fourier analysis developed by Howell, presented in an elegant series of papers [2-6] n supporting the Fourier transformation of the functions on R . This theory is similar to the theory for tempered distributions and to some extent, can be viewed as an extension of the Fourier theory. Bhosale [1] had extended Fractional Fourier transform on Howell’s space. Mahalle et. al. [7, 8] described a new theory of Mellin and Laplace transform defined on Howell’s space. -
Quantum Physics in Space
Quantum Physics in Space Alessio Belenchiaa,b,∗∗, Matteo Carlessob,c,d,∗∗, Omer¨ Bayraktare,f, Daniele Dequalg, Ivan Derkachh, Giulio Gasbarrii,j, Waldemar Herrk,l, Ying Lia Lim, Markus Rademacherm, Jasminder Sidhun, Daniel KL Oin, Stephan T. Seidelo, Rainer Kaltenbaekp,q, Christoph Marquardte,f, Hendrik Ulbrichtj, Vladyslav C. Usenkoh, Lisa W¨ornerr,s, Andr´eXuerebt, Mauro Paternostrob, Angelo Bassic,d,∗ aInstitut f¨urTheoretische Physik, Eberhard-Karls-Universit¨atT¨ubingen, 72076 T¨ubingen,Germany bCentre for Theoretical Atomic,Molecular, and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom cDepartment of Physics,University of Trieste, Strada Costiera 11, 34151 Trieste,Italy dIstituto Nazionale di Fisica Nucleare, Trieste Section, Via Valerio 2, 34127 Trieste, Italy eMax Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany fInstitute of Optics, Information and Photonics, Friedrich-Alexander University Erlangen-N¨urnberg, Staudtstraße 7 B2, 91058 Erlangen, Germany gScientific Research Unit, Agenzia Spaziale Italiana, Matera, Italy hDepartment of Optics, Palacky University, 17. listopadu 50,772 07 Olomouc,Czech Republic iF´ısica Te`orica: Informaci´oi Fen`omensQu`antics,Department de F´ısica, Universitat Aut`onomade Barcelona, 08193 Bellaterra (Barcelona), Spain jDepartment of Physics and Astronomy, University of Southampton, Highfield Campus, SO17 1BJ, United Kingdom kDeutsches Zentrum f¨urLuft- und Raumfahrt e. V. (DLR), Institut f¨urSatellitengeod¨asieund -
1 Temporal Arrows in Space-Time Temporality
Temporal Arrows in Space-Time Temporality (…) has nothing to do with mechanics. It has to do with statistical mechanics, thermodynamics (…).C. Rovelli, in Dieks, 2006, 35 Abstract The prevailing current of thought in both physics and philosophy is that relativistic space-time provides no means for the objective measurement of the passage of time. Kurt Gödel, for instance, denied the possibility of an objective lapse of time, both in the Special and the General theory of relativity. From this failure many writers have inferred that a static block universe is the only acceptable conceptual consequence of a four-dimensional world. The aim of this paper is to investigate how arrows of time could be measured objectively in space-time. In order to carry out this investigation it is proposed to consider both local and global arrows of time. In particular the investigation will focus on a) invariant thermodynamic parameters in both the Special and the General theory for local regions of space-time (passage of time); b) the evolution of the universe under appropriate boundary conditions for the whole of space-time (arrow of time), as envisaged in modern quantum cosmology. The upshot of this investigation is that a number of invariant physical indicators in space-time can be found, which would allow observers to measure the lapse of time and to infer both the existence of an objective passage and an arrow of time. Keywords Arrows of time; entropy; four-dimensional world; invariance; space-time; thermodynamics 1 I. Introduction Philosophical debates about the nature of space-time often centre on questions of its ontology, i.e. -
Gravitational Redshift in Quantum-Clock Interferometry
PHYSICAL REVIEW X 10, 021014 (2020) Gravitational Redshift in Quantum-Clock Interferometry Albert Roura Institute of Quantum Technologies, German Aerospace Center (DLR), Söflinger Straße 100, 89077 Ulm, Germany and Institut für Quantenphysik, Universität Ulm, Albert-Einstein-Allee 11, 89081 Ulm, Germany (Received 29 September 2019; revised manuscript received 12 February 2020; accepted 5 March 2020; published 20 April 2020) The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field. All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times. This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations. -
Memristor-Based Approximation of Gaussian Filter
Memristor-based Approximation of Gaussian Filter Alex Pappachen James, Aidyn Zhambyl, Anju Nandakumar Electrical and Computer Engineering department Nazarbayev University School of Engineering Astana, Kazakhstan Email: [email protected], [email protected], [email protected] Abstract—Gaussian filter is a filter with impulse response of fourth section some mathematical analysis will be provided to Gaussian function. These filters are useful in image processing obtained results and finally the paper will be concluded by of 2D signals, as it removes unnecessary noise. Also, they could stating the result of the done work. be helpful for data transmission (e.g. GMSK modulation). In practice, the Gaussian filters could be approximately designed II. GAUSSIAN FILTER AND MEMRISTOR by several methods. One of these methods are to construct Gaussian-like filter with the help of memristors and RLC circuits. A. Gaussian Filter Therefore, the objective of this project is to find and design Gaussian filter is such filter which convolves the input signal appropriate model of Gaussian-like filter, by using mentioned devices. Finally, one possible model of Gaussian-like filter based with the impulse response of Gaussian function. In some on memristor designed and analysed in this paper. sources this process is also known as the Weierstrass transform [2]. The Gaussian function is given as in equation 1, where µ Index Terms—Gaussian filters, analog filter, memristor, func- is the time shift and σ is the scale. For input signal of x(t) tion approximation the output is the convolution of x(t) with Gaussian, as shown in equation 2.