Enhancing User Privacy in SARG04-Based Private Database Query Protocols
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Free-Electron Qubits
Free-Electron Qubits Ori Reinhardt†, Chen Mechel†, Morgan Lynch, and Ido Kaminer Department of Electrical Engineering and Solid State Institute, Technion - Israel Institute of Technology, 32000 Haifa, Israel † equal contributors Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons’ energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit’s non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times. Most platforms for quantum computation today rely on light-matter interactions of bound electrons such as in ion traps [1], superconducting circuits [2], and electron spin systems [3,4]. These form a natural choice for implementing 2-level systems with spin algebra. Instead of using bound electrons for quantum information processing, in this letter we propose using free electrons and manipulating them with femtosecond laser pulses in optical frequencies. Compared to bound electrons, free electron systems enable accessing high energy scales and short time scales. Moreover, they possess quantized degrees of freedom that can take unbounded values, such as orbital angular momentum (OAM), which has also been proposed for information encoding [5-10]. Analogously, photons also have the capability to encode information in their OAM [11,12]. -
Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect
Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect A. A. Suratgar1, S. Rafiei*2, A. A. Taherpour3, A. Babaei4 1 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran. 1 Assistant Professor, Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran. 2 Young Researchers Club, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran. *[email protected] 3 Professor, Chemistry Department, Faculty of Science, Islamic Azad University, Arak Branch, Arak, Iran. 4 faculty member of Islamic Azad University, Khomein Branch, Khomein, ABSTRACT In this paper we present a new method for designing a qubit and decoder in quantum computing based on the field effect in nuclear spin. In this method, the position of hydrogen has been studied in different external fields. The more we have different external field effects and electromagnetic radiation, the more we have different distribution ratios. Consequently, the quality of different distribution ratios has been applied to the suggested qubit and decoder model. We use the nuclear property of hydrogen in order to find a logical truth value. Computational results demonstrate the accuracy and efficiency that can be obtained with the use of these models. Keywords: quantum computing, qubit, decoder, gyromagnetic ratio, spin. 1. Introduction different hydrogen atoms in compound applied for the qubit and decoder designing. Up to now many papers deal with the possibility to realize a reversible computer based on the laws of 2. An overview on quantum concepts quantum mechanics [1]. In this chapter a short introduction is presented Modern quantum chemical methods provide into the interesting field of quantum in physics, powerful tools for theoretical modeling and Moore´s law and a summary of the quantum analysis of molecular electronic structures. -
A Theoretical Study of Quantum Memories in Ensemble-Based Media
A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz St. Hugh's College, Oxford A thesis submitted to the Mathematical and Physical Sciences Division for the degree of Doctor of Philosophy in the University of Oxford Michaelmas Term, 2007 Atomic and Laser Physics, University of Oxford i A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz, St. Hugh's College, Oxford Michaelmas Term 2007 Abstract The transfer of information from flying qubits to stationary qubits is a fundamental component of many quantum information processing and quantum communication schemes. The use of photons, which provide a fast and robust platform for encoding qubits, in such schemes relies on a quantum memory in which to store the photons, and retrieve them on-demand. Such a memory can consist of either a single absorber, or an ensemble of absorbers, with a ¤-type level structure, as well as other control ¯elds that a®ect the transfer of the quantum signal ¯eld to a material storage state. Ensembles have the advantage that the coupling of the signal ¯eld to the medium scales with the square root of the number of absorbers. In this thesis we theoretically study the use of ensembles of absorbers for a quantum memory. We characterize a general quantum memory in terms of its interaction with the signal and control ¯elds, and propose a ¯gure of merit that measures how well such a memory preserves entanglement. We derive an analytical expression for the entanglement ¯delity in terms of fluctuations in the stochastic Hamiltonian parameters, and show how this ¯gure could be measured experimentally. -
Security of Quantum Key Distribution with Multiphoton Components
Security of quantum key distribution with multiphoton components 1,2, 1,2, 1,2 1,2 Hua-Lei Yin ∗, Yao Fu ∗, Yingqiu Mao & Zeng-Bing Chen 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2The CAS Center for Excellence in QIQP and the Synergetic Innovation Center for QIQP, Uni- versity of Science and Technology of China, Hefei, Anhui 230026, China ∗ These authors contributed equally to this work. Correspondence and requests for materials should be addressed to H.-L.Y. (email: [email protected]) or Z.-B.C. (email: [email protected]) Most qubit-based quantum key distribution (QKD) protocols extract the secure key merely from single-photon component of the attenuated lasers. However, with the Scarani-Acin- Ribordy-Gisin 2004 (SARG04) QKD protocol, the unconditionally secure key can be ex- tracted from the two-photon component by modifying the classical post-processing proce- dure in the BB84 protocol. Employing the merits of SARG04 QKD protocol and six-state preparation, one can extract secure key from the components of single photon up to four arXiv:1607.02366v1 [quant-ph] 8 Jul 2016 photons. In this paper, we provide the exact relations between the secure key rate and the bit error rate in a six-state SARG04 protocol with single-photon, two-photon, three- photon, and four-photon sources. By restricting the mutual information between the phase error and bit error, we obtain a higher secure bit error rate threshold of the multiphoton components than previous works. -
Quantum Key Distribution Protocols and Applications
Quantum Key Distribution Protocols and Applications Sheila Cobourne Technical Report RHUL{MA{2011{05 8th March 2011 Department of Mathematics Royal Holloway, University of London Egham, Surrey TW20 0EX, England http://www.rhul.ac.uk/mathematics/techreports Title: Quantum Key Distribution – Protocols and Applications Name: Sheila Cobourne Student Number: 100627811 Supervisor: Carlos Cid Submitted as part of the requirements for the award of the MSc in Information Security at Royal Holloway, University of London. I declare that this assignment is all my own work and that I have acknowledged all quotations from the published or unpublished works of other people. I declare that I have also read the statements on plagiarism in Section 1 of the Regulations Governing Examination and Assessment Offences and in accordance with it I submit this project report as my own work. Signature: Date: Acknowledgements I would like to thank Carlos Cid for his helpful suggestions and guidance during this project. Also, I would like to express my appreciation to the lecturers at Royal Holloway who have increased my understanding of Information Security immensely over the course of the MSc, without which this project would not have been possible. Contents Table of Figures ................................................................................................... 6 Executive Summary ............................................................................................. 7 Chapter 1 Introduction ................................................................................... -
Physical Implementations of Quantum Computing
Physical implementations of quantum computing Andrew Daley Department of Physics and Astronomy University of Pittsburgh Overview (Review) Introduction • DiVincenzo Criteria • Characterising coherence times Survey of possible qubits and implementations • Neutral atoms • Trapped ions • Colour centres (e.g., NV-centers in diamond) • Electron spins (e.g,. quantum dots) • Superconducting qubits (charge, phase, flux) • NMR • Optical qubits • Topological qubits Back to the DiVincenzo Criteria: Requirements for the implementation of quantum computation 1. A scalable physical system with well characterized qubits 1 | i 0 | i 2. The ability to initialize the state of the qubits to a simple fiducial state, such as |000...⟩ 1 | i 0 | i 3. Long relevant decoherence times, much longer than the gate operation time 4. A “universal” set of quantum gates control target (single qubit rotations + C-Not / C-Phase / .... ) U U 5. A qubit-specific measurement capability D. P. DiVincenzo “The Physical Implementation of Quantum Computation”, Fortschritte der Physik 48, p. 771 (2000) arXiv:quant-ph/0002077 Neutral atoms Advantages: • Production of large quantum registers • Massive parallelism in gate operations • Long coherence times (>20s) Difficulties: • Gates typically slower than other implementations (~ms for collisional gates) (Rydberg gates can be somewhat faster) • Individual addressing (but recently achieved) Quantum Register with neutral atoms in an optical lattice 0 1 | | Requirements: • Long lived storage of qubits • Addressing of individual qubits • Single and two-qubit gate operations • Array of singly occupied sites • Qubits encoded in long-lived internal states (alkali atoms - electronic states, e.g., hyperfine) • Single-qubit via laser/RF field coupling • Entanglement via Rydberg gates or via controlled collisions in a spin-dependent lattice Rb: Group II Atoms 87Sr (I=9/2): Extensively developed, 1 • P1 e.g., optical clocks 3 • Degenerate gases of Yb, Ca,.. -
Electron Spin Qubits in Quantum Dots
Electron spin qubits in quantum dots R. Hanson, J.M. Elzerman, L.H. Willems van Beveren, L.M.K. Vandersypen, and L.P. Kouwenhoven' 'Kavli Institute of NanoScience Delft, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands (Dated: September 24, 2004) We review our experimental progress on the spintronics proposal for quantum computing where the quantum bits (quhits) are implemented with electron spins confined in semiconductor quantum dots. Out of the five criteria for a scalable quantum computer, three have already been satisfied. We have fabricated and characterized a double quantum dot circuit with an integrated electrometer. The dots can be tuned to contain a single electron each. We have resolved the two basis states of the qubit by electron transport measurements. Furthermore, initialization and singleshot read-out of the spin statc have been achieved. The single-spin relaxation time was found to be very long, but the decoherence time is still unknown. We present concrete ideas on how to proceed towards coherent spin operations and two-qubit operations. PACS numbers: INTRODUCTION depicted in Fig. la. In Fig. 1b we map out the charging diagram of the The interest in quantum computing [l]derives from double dot using the electrometer. Horizontal (vertical) the hope to outperform classical computers using new lines in this diagram correspond to changes in the number quantum algorithms. A natural candidate for the qubit of electrons in the left (right) dot. In the top right of the is the electron spin because the only two possible spin figure lines are absent, indicating that the double dot orientations 17) and 11) correspond to the basis states of is completely depleted of electrons. -
Basic Probability Theory A
Basic Probability Theory A In order to follow many of the arguments in these notes, especially when talking about entropies, it is necessary to have some basic knowledge of probability theory. Therefore, we review here the most important tools of probability theory that are used. One of the basic notions of probability theory that also frequently appears throughout these notes is that of a discrete random variable. A random variable X can take one of several values, the so-called realizations x,givenbythealphabet X. The probability that a certain realization x ∈ X occurs is given by the probability distribution pX(x). We usually use upper case letters to denote the random variable, lower case letters to denote realizations thereof, and calligraphic letters to denote the alphabet. Suppose we have two random variables X and Y , which may depend on each other. We can then define the joint probability distribution pX,Y (x, y) of X and Y that tells you the probability that Y = y and X = x. This notion (and the following definition) can be expanded to n random variables, but we restrict ourselves to the case of pairs X, Y here to keep the notation simple. Given the joint probability distribution of the pair X, Y , we can derive the marginal distribution PX(x) by pX(x) = pX,Y (x, y) ∀ x ∈ X (A.1) y∈Y and analogously for PY (y). The two random variables X and Y are said to be independent if pX,Y (x, y) = pX(x)pY (y). (A.2) © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 219 R. -
Quantum Computing : a Gentle Introduction / Eleanor Rieffel and Wolfgang Polak
QUANTUM COMPUTING A Gentle Introduction Eleanor Rieffel and Wolfgang Polak The MIT Press Cambridge, Massachusetts London, England ©2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email [email protected] This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, 1965– Quantum computing : a gentle introduction / Eleanor Rieffel and Wolfgang Polak. p. cm.—(Scientific and engineering computation) Includes bibliographical references and index. ISBN 978-0-262-01506-6 (hardcover : alk. paper) 1. Quantum computers. 2. Quantum theory. I. Polak, Wolfgang, 1950– II. Title. QA76.889.R54 2011 004.1—dc22 2010022682 10987654321 Contents Preface xi 1 Introduction 1 I QUANTUM BUILDING BLOCKS 7 2 Single-Qubit Quantum Systems 9 2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol 18 2.5 The State Space of a Single-Qubit System 21 2.5.1 Relative Phases versus Global Phases 21 2.5.2 Geometric Views of the State Space of a Single Qubit 23 2.5.3 Comments on General Quantum State Spaces -
Computational Difficulty of Computing the Density of States
Computational Difficulty of Computing the Density of States Brielin Brown,1, 2 Steven T. Flammia,2 and Norbert Schuch3 1University of Virginia, Departments of Physics and Computer Science, Charlottesville, Virginia 22904, USA 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada 3California Institute of Technology, Institute for Quantum Information, MC 305-16, Pasadena, California 91125, USA We study the computational difficulty of computing the ground state degeneracy and the density of states for local Hamiltonians. We show that the difficulty of both problems is exactly captured by a class which we call #BQP, which is the counting version of the quantum complexity class QMA. We show that #BQP is not harder than its classical counting counterpart #P, which in turn implies that computing the ground state degeneracy or the density of states for classical Hamiltonians is just as hard as it is for quantum Hamiltonians. Understanding the physical properties of correlated quantum computer. We show that both problems, com- quantum many-body systems is a problem of central im- puting the density of states and counting the ground state portance in condensed matter physics. The density of degeneracy, are complete problems for the class #BQP, states, defined as the number of energy eigenstates per i.e., they are among the hardest problems in this class. energy interval, plays a particularly crucial role in this Having quantified the difficulty of computing the den- endeavor. It is a key ingredient when deriving many sity of states and counting the number of ground states, thermodynamic properties from microscopic models, in- we proceed to relate #BQP to known classical counting cluding specific heat capacity, thermal conductivity, band complexity classes, and show that #BQP equals #P (un- structure, and (near the Fermi energy) most electronic der weakly parsimonious reductions). -
Intercept-Resend Attack on SARG04 Protocol: an Extended Work
Polytechnic Journal. 2020. 10(1): 88-92 ISSN: 2313-5727 http://journals.epu.edu.iq/index.php/polytechnic RESEARCH ARTICLE Intercept-Resend Attack on SARG04 Protocol: An Extended Work Ali H. Yousif*, Omar S. Mustafa, Dana F. Abdulqadir, Farah S. Khoshaba Department of Information System Engineering, Erbil Technical Engineering College, Erbil Polytechnic University, Erbil, Kurdistan Region, Iraq *Correspondence author: ABSTRACT Ali H. Yousif, Department of Information In this paper, intercept/resend eavesdropper attack over SARG04 quantum key distribution protocol is System Engineering, investigated by bounding the information of an eavesdropper; then, the attack has been analyzed. In Erbil Technical Engineering 2019, simulation and enhancement of the performance of SARG04 protocol have been done by the College, Erbil Polytechnic same research group in terms of error correction stage using multiparity rather than single parity (Omar, University, Erbil, Kurdistan 2019). The probability of detecting the case in the random secret key by eavesdropper is estimated. Region, Iraq, The results of intercept/resend eavesdropper attack proved that the attack has a significant impact E-mail: [email protected] on the operation of the SARG04 protocol in terms of the final key length. Received: 28 October 2019 Keywords: Eavesdropper; Intercept-resend; IR; Quantum; SARG04 Accepted: 05 February 2020 Published: 30 June 2020 DOI 10.25156/ptj.v10n1y2020.pp88-92 INTRODUCTION promises to revolutionize secure communication using the key distribution. Nowadays, the information security is the most important concern of people and entity. One of the main issues Quantum key distribution (QKD) enables two parties to of practical quantum communication is the information establish a secure random secret key depending on the security under the impact of disturbances or quantum principles of quantum mechanics. -
Distinguishing Different Classes of Entanglement for Three Qubit Pure States
Distinguishing different classes of entanglement for three qubit pure states Chandan Datta Institute of Physics, Bhubaneswar [email protected] YouQu-2017, HRI Chandan Datta (IOP) Tripartite Entanglement YouQu-2017, HRI 1 / 23 Overview 1 Introduction 2 Entanglement 3 LOCC 4 SLOCC 5 Classification of three qubit pure state 6 A Teleportation Scheme 7 Conclusion Chandan Datta (IOP) Tripartite Entanglement YouQu-2017, HRI 2 / 23 Introduction History In 1935, Einstein, Podolsky and Rosen (EPR)1 encountered a spooky feature of quantum mechanics. Apparently, this feature is the most nonclassical manifestation of quantum mechanics. Later, Schr¨odingercoined the term entanglement to describe the feature2. The outcome of the EPR paper is that quantum mechanical description of physical reality is not complete. Later, in 1964 Bell formalized the idea of EPR in terms of local hidden variable model3. He showed that any local realistic hidden variable theory is inconsistent with quantum mechanics. 1Phys. Rev. 47, 777 (1935). 2Naturwiss. 23, 807 (1935). 3Physics (Long Island City, N.Y.) 1, 195 (1964). Chandan Datta (IOP) Tripartite Entanglement YouQu-2017, HRI 3 / 23 Introduction Motivation It is an essential resource for many information processing tasks, such as quantum cryptography4, teleportation5, super-dense coding6 etc. With the recent advancement in this field, it is clear that entanglement can perform those task which is impossible using a classical resource. Also from the foundational perspective of quantum mechanics, entanglement is unparalleled for its supreme importance. Hence, its characterization and quantification is very important from both theoretical as well as experimental point of view. 4Rev. Mod. Phys. 74, 145 (2002).