Decoherence and Open Quantum Systems 33 4.1 from Closed to Open Quantum Systems
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The Theory of Quantum Coherence María García Díaz
ADVERTIMENT. Lʼaccés als continguts dʼaquesta tesi queda condicionat a lʼacceptació de les condicions dʼús establertes per la següent llicència Creative Commons: http://cat.creativecommons.org/?page_id=184 ADVERTENCIA. El acceso a los contenidos de esta tesis queda condicionado a la aceptación de las condiciones de uso establecidas por la siguiente licencia Creative Commons: http://es.creativecommons.org/blog/licencias/ WARNING. The access to the contents of this doctoral thesis it is limited to the acceptance of the use conditions set by the following Creative Commons license: https://creativecommons.org/licenses/?lang=en Universitat Aut`onomade Barcelona The theory of quantum coherence by Mar´ıaGarc´ıaD´ıaz under supervision of Prof. Andreas Winter A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in Unitat de F´ısicaTe`orica:Informaci´oi Fen`omensQu`antics Departament de F´ısica Facultat de Ci`encies Bellaterra, December, 2019 “The arts and the sciences all draw together as the analyst breaks them down into their smallest pieces: at the hypothetical limit, at the very quick of epistemology, there is convergence of speech, picture, song, and instigating force.” Daniel Albright, Quantum poetics: Yeats, Pound, Eliot, and the science of modernism Abstract Quantum coherence, or the property of systems which are in a superpo- sition of states yielding interference patterns in suitable experiments, is the main hallmark of departure of quantum mechanics from classical physics. Besides its fascinating epistemological implications, quantum coherence also turns out to be a valuable resource for quantum information tasks, and has even been used in the description of fundamental biological processes. -
A Closure Scheme for Chemical Master Equations
A closure scheme for chemical master equations Patrick Smadbeck and Yiannis N. Kaznessis1 Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455 Edited by Wing Hung Wong, Stanford University, Stanford, CA, and approved July 16, 2013 (received for review April 8, 2013) Probability reigns in biology, with random molecular events dictating equation governs the evolution of the probability, PðX; tÞ,thatthe the fate of individual organisms, and propelling populations of system is at state X at time t: species through evolution. In principle, the master probability À Á equation provides the most complete model of probabilistic behavior ∂P X; t X À Á À Á À Á À Á = T X X′ P X′; t − T X′ X P X; t : [1] in biomolecular networks. In practice, master equations describing ∂t complex reaction networks have remained unsolved for over 70 X′ years. This practical challenge is a reason why master equations, for À Á all their potential, have not inspired biological discovery. Herein, we This is a probability conservation equation, where T X X′ is present a closure scheme that solves the master probability equation the transition propensity from any possible state X′ to state X of networks of chemical or biochemical reactions. We cast the master per unit time. In a network of chemical or biochemical reactions, equation in terms of ordinary differential equations that describe the the transition probabilities are defined by the reaction-rate laws time evolution of probability distribution moments. We postulate as a set of Poisson-distributed reaction propensities; these simply that a finite number of moments capture all of the necessary dictate how many reaction events take place per unit time. -
Energy Conservation and the Correlation Quasi-Temperature in Open Quantum Dynamics
Article Energy Conservation and the Correlation Quasi-Temperature in Open Quantum Dynamics Vladimir Morozov 1 and Vasyl’ Ignatyuk 2,* 1 MIREA-Russian Technological University, Vernadsky Av. 78, 119454 Moscow, Russia; [email protected] 2 Institute for Condensed Matter Physics, Svientsitskii Str. 1, 79011 Lviv, Ukraine * Correspondence: [email protected]; Tel.: +38-032-276-1054 Received: 25 October 2018; Accepted: 27 November 2018; Published: 30 November 2018 Abstract: The master equation for an open quantum system is derived in the weak-coupling approximation when the additional dynamical variable—the mean interaction energy—is included into the generic relevant statistical operator. This master equation is nonlocal in time and involves the “quasi-temperature”, which is a non- equilibrium state parameter conjugated thermodynamically to the mean interaction energy of the composite system. The evolution equation for the quasi-temperature is derived using the energy conservation law. Thus long-living dynamical correlations, which are associated with this conservation law and play an important role in transition to the Markovian regime and subsequent equilibration of the system, are properly taken into account. Keywords: open quantum system; master equation; non-equilibrium statistical operator; relevant statistical operator; quasi-temperature; dynamic correlations 1. Introduction In this paper, we continue the study of memory effects and nonequilibrium correlations in open quantum systems, which was initiated recently in Reference [1]. In the cited paper, the nonequilibrium statistical operator method (NSOM) developed by Zubarev [2–5] was used to derive the non-Markovian master equation for an open quantum system, taking into account memory effects and the evolution of an additional “relevant” variable—the mean interaction energy of the composite system (the open quantum system plus its environment). -
Arxiv:Quant-Ph/0105127V3 19 Jun 2003
DECOHERENCE, EINSELECTION, AND THE QUANTUM ORIGINS OF THE CLASSICAL Wojciech Hubert Zurek Theory Division, LANL, Mail Stop B288 Los Alamos, New Mexico 87545 Decoherence is caused by the interaction with the en- A. The problem: Hilbert space is big 2 vironment which in effect monitors certain observables 1. Copenhagen Interpretation 2 of the system, destroying coherence between the pointer 2. Many Worlds Interpretation 3 B. Decoherence and einselection 3 states corresponding to their eigenvalues. This leads C. The nature of the resolution and the role of envariance4 to environment-induced superselection or einselection, a quantum process associated with selective loss of infor- D. Existential Interpretation and ‘Quantum Darwinism’4 mation. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite II. QUANTUM MEASUREMENTS 5 of the environment. Einselection enforces classicality by A. Quantum conditional dynamics 5 imposing an effective ban on the vast majority of the 1. Controlled not and a bit-by-bit measurement 6 Hilbert space, eliminating especially the flagrantly non- 2. Measurements and controlled shifts. 7 local “Schr¨odinger cat” states. Classical structure of 3. Amplification 7 B. Information transfer in measurements 9 phase space emerges from the quantum Hilbert space in 1. Action per bit 9 the appropriate macroscopic limit: Combination of einse- C. “Collapse” analogue in a classical measurement 9 lection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselec- III. CHAOS AND LOSS OF CORRESPONDENCE 11 tion replaces quantum entanglement between the appa- A. Loss of the quantum-classical correspondence 11 B. -
The Quantum Toolbox in Python Release 2.2.0
QuTiP: The Quantum Toolbox in Python Release 2.2.0 P.D. Nation and J.R. Johansson March 01, 2013 CONTENTS 1 Frontmatter 1 1.1 About This Documentation.....................................1 1.2 Citing This Project..........................................1 1.3 Funding................................................1 1.4 Contributing to QuTiP........................................2 2 About QuTiP 3 2.1 Brief Description...........................................3 2.2 Whats New in QuTiP Version 2.2..................................4 2.3 Whats New in QuTiP Version 2.1..................................4 2.4 Whats New in QuTiP Version 2.0..................................4 3 Installation 7 3.1 General Requirements........................................7 3.2 Get the software...........................................7 3.3 Installation on Ubuntu Linux.....................................8 3.4 Installation on Mac OS X (10.6+)..................................9 3.5 Installation on Windows....................................... 10 3.6 Verifying the Installation....................................... 11 3.7 Checking Version Information via the About Box.......................... 11 4 QuTiP Users Guide 13 4.1 Guide Overview........................................... 13 4.2 Basic Operations on Quantum Objects................................ 13 4.3 Manipulating States and Operators................................. 20 4.4 Using Tensor Products and Partial Traces.............................. 29 4.5 Time Evolution and Quantum System Dynamics......................... -
Fluctuations of Spacetime and Holographic Noise in Atomic Interferometry
General Relativity and Gravitation (2011) DOI 10.1007/s10714-010-1137-7 RESEARCHARTICLE Ertan Gokl¨ u¨ · Claus Lammerzahl¨ Fluctuations of spacetime and holographic noise in atomic interferometry Received: 10 December 2009 / Accepted: 12 December 2010 c Springer Science+Business Media, LLC 2010 Abstract On small scales spacetime can be understood as some kind of space- time foam of fluctuating bubbles or loops which are expected to be an outcome of a theory of quantum gravity. One recently discussed model for this kind of space- time fluctuations is the holographic principle which allows to deduce the structure of these fluctuations. We review and discuss two scenarios which rely on the holo- graphic principle leading to holographic noise. One scenario leads to fluctuations of the spacetime metric affecting the dynamics of quantum systems: (i) an appar- ent violation of the equivalence principle, (ii) a modification of the spreading of wave packets, and (iii) a loss of quantum coherence. All these effects can be tested with cold atoms. Keywords Quantum gravity phenomenology, Holographic principle, Spacetime fluctuations, UFF, Decoherence, Wavepacket dynamics 1 Introduction The unification of quantum mechanics and General Relativity is one of the most outstanding problems of contemporary physics. Though yet there is no theory of quantum gravity. There are a lot of reasons why gravity must be quantized [33]. For example, (i) because of the fact that all matter fields are quantized the interactions, generated by theses fields, must also be quantized. (ii) In quantum mechanics and General Relativity the notion of time is completely different. (iii) Generally, in General Relativity singularities necessarily appear where physical laws are not valid anymore. -
Non-Ergodicity in Open Quantum Systems Through Quantum Feedback
epl draft Non-Ergodicity in open quantum systems through quantum feedback Lewis A. Clark,1;4 Fiona Torzewska,2;4 Ben Maybee3;4 and Almut Beige4 1 Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle-Upon-Tyne, NE1 7RU, United Kingdom 2 The School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom 3 Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, UK, United Kingdom 4 The School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom PACS 42.50.-p { Quantum optics PACS 42.50.Ar { Photon statistics and coherence theory PACS 42.50.Lc { Quantum fluctuations, quantum noise, and quantum jumps Abstract {It is well known that quantum feedback can alter the dynamics of open quantum systems dramatically. In this paper, we show that non-Ergodicity may be induced through quan- tum feedback and resultantly create system dynamics that have lasting dependence on initial conditions. To demonstrate this, we consider an optical cavity inside an instantaneous quantum feedback loop, which can be implemented relatively easily in the laboratory. Non-Ergodic quantum systems are of interest for applications in quantum information processing, quantum metrology and quantum sensing and could potentially aid the design of thermal machines whose efficiency is not limited by the laws of classical thermodynamics. Introduction. { Looking at the mechanical motion applicability of statistical-mechanical methods to quan- of individual particles, it is hard to see why ensembles tum physics [3]. Moreover, it has been shown that open of such particles should ever thermalise. -
Neural Networks Take on Open Quantum Systems
VIEWPOINT Neural Networks Take on Open Quantum Systems Simulating a quantum system that exchanges energy with the outside world is notoriously hard, but the necessary computations might be easier with the help of neural networks. by Maria Schuld∗,y, Ilya Sinayskiyyy, and Francesco Petruccione{,k,∗∗ eural networks are behind technologies that are revolutionizing our daily lives, such as face recognition, web searching, and medical diagno- sis. These general problem solvers reach their Nsolutions by being adapted or “trained” to capture cor- relations in real-world data. Having seen the success of neural networks, physicists are asking if the tools might also be useful in areas ranging from high-energy physics to quantum computing [1]. Four research groups now re- port on using neural network tools to tackle one of the most Figure 1: Four teams have designed a neural network (right) that computationally challenging problems in condensed-matter can find the stationary steady states for an ``open'' quantum physics—simulating the behavior of an open many-body system (left). Their approach is built on neural network models for quantum system [2–5]. This scenario describes a collection of closed systems, where the wave function was represented by a particles—such as the qubits in a quantum computer—that statistical distribution over ``visible spins'' connected to a number of ``hidden spins.'' To extend the idea to an open system, three of both interact with each other and exchange energy with their the teams [3–5] added in a third set of ``ancillary spins,'' which environment. For certain open systems, the new work might capture correlations between the system and environment. -
Study of Decoherence in Quantum Computers: a Circuit-Design Perspective
Study of Decoherence in Quantum Computers: A Circuit-Design Perspective Abdullah Ash- Saki Mahabubul Alam Swaroop Ghosh Electrical Engineering Electrical Engineering Electrical Engineering Pennsylvania State University Pennsylvania State University Pennsylvania State University University Park, USA University Park, USA University Park, USA [email protected] [email protected] [email protected] Abstract—Decoherence of quantum states is a major hurdle interaction with environment [8]. The decoherence problem towards scalable and reliable quantum computing. Lower de- worsens with an increasing number of qubits. To mitigate coherence (i.e., higher fidelity) can alleviate the error correc- those, techniques like cryogenic cooling and error correction tion overhead and obviate the need for energy-intensive noise reduction techniques e.g., cryogenic cooling. In this paper, we code [9] are employed. However, these techniques are costly performed a noise-induced decoherence analysis of single and as cooling the qubits to ultra-low temperature (mili-Kelvin) re- multi-qubit quantum gates using physics-based simulations. The quires very high power (as much as 25kW) and error correction analysis indicates that (i) decoherence depends on the input requires many redundant physical qubits (one popular error state and the gate type. Larger number of j1i states worsen correction method named surface code incurs 18X overhead the decoherence; (ii) amplitude damping is more detrimental than phase damping; (iii) shorter depth implementation of a [10]). quantum function can achieve lower decoherence. Simulations Circuit level implications of decoherence are not well un- indicate 20% improvement in the fidelity of a quantum adder derstood. Therefore, a circuit level analysis of decoherence when realized using lower depth topology. -
Semi-Classical Lindblad Master Equation for Spin Dynamics
Journal of Physics A: Mathematical and Theoretical J. Phys. A: Math. Theor. 54 (2021) 235201 (13pp) https://doi.org/10.1088/1751-8121/abf79b Semi-classical Lindblad master equation for spin dynamics Jonathan Dubois∗ ,UlfSaalmann and Jan M Rost Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany E-mail: [email protected], [email protected] and [email protected] Received 25 January 2021, revised 18 March 2021 Accepted for publication 13 April 2021 Published 7 May 2021 Abstract We derive the semi-classical Lindblad master equation in phase space for both canonical and non-canonicalPoisson brackets using the Wigner–Moyal formal- ism and the Moyal star-product. The semi-classical limit for canonical dynam- ical variables, i.e. canonical Poisson brackets, is the Fokker–Planck equation, as derived before. We generalize this limit and show that it holds also for non- canonical Poisson brackets. Examples are gyro-Poisson brackets, which occur in spin ensembles, systems of recent interest in atomic physics and quantum optics. We show that the equations of motion for the collective spin variables are given by the Bloch equations of nuclear magnetization with relaxation. The Bloch and relaxation vectors are expressed in terms of the microscopic operators: the Hamiltonian and the Lindblad functions in the Wigner–Moyal formalism. Keywords: Lindblad master equations,non-canonicalvariables,Hamiltonian systems, spin systems, classical and semi-classical limit, thermodynamical limit (Some fgures may appear in colour only in the online journal) 1. Lindblad quantum master equation Since perfect isolation of a system is an idealization [1, 2], open microscopic systems, which interact with an environment, are prevalent in nature as well as in experiments. -
Quantum Thermodynamics of Single Particle Systems Md
www.nature.com/scientificreports OPEN Quantum thermodynamics of single particle systems Md. Manirul Ali, Wei‑Ming Huang & Wei‑Min Zhang* Thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two‑level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system‑reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system‑reservoir coupling regime where the Born‑Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non- Markovian memory efect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by infationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The infationary dynamics may also relate to the origin of big bang and universe infation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved. In the past decade, many eforts have been devoted to understand how, starting from an isolated quantum system evolving under Hamiltonian dynamics, equilibration and efective thermodynamics emerge at long times1–5. -
Arxiv:2103.12042V3 [Quant-Ph] 25 Jul 2021 Approximation)
Unified Gorini{Kossakowski{Lindblad{Sudarshan quantum master equation beyond the secular approximation Anton Trushechkin1, 2 1Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia 2National University of Science and Technology MISIS, Moscow 119049, Russia∗ (Dated: July 27, 2021) Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini{Kossakowski{ Lindblad{Sudarshan form (in particular, it preserves positivity of the density operator) and also satisfies the standard thermodynamic properties is a known long-standing problem in theory of open quantum systems. The nonsecular terms are important when some energy levels of the system or their differences (Bohr frequencies) are nearly degenerate. We provide a fully rigorous derivation of such equation based on a formalization of the weak-coupling limit for the general case. I. INTRODUCTION particular, does not preserve positivity of the density op- erator, thus leading to unphysical predictions. Also, this Quantum master equations are at the heart of theory of equation does not have the mentioned thermodynamic open quantum systems [1{3]. They describe the dynam- properties. ics of the reduced density operator of a system interact- Derivation of a mathematically correct quantum mas- ing with the environment (\bath") and are widely used ter equation which takes into account nonsecular effects in quantum optics, condensed matter physics, charge and is actively studied. Several heuristic approaches turning energy transfer in molecular systems, bio-chemical pro- the Redfield equation into an equation of the GKLS form cesses [4], quantum thermodynamics [5,6], etc.