DOCSLIB.ORG

Machine Learning for Long-Distance Quantum Communication

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Machine Learning for Long-Distance Quantum Communication Machine learning for long-distance quantum communication Julius Walln¨ofer,1, 2 Alexey A. Melnikov,2, 3, 4 Wolfgang D¨ur,2 and Hans J. Briegel2, 5 1Department of Physics, Freie Universit¨atBerlin, Arnimallee 14, 14195 Berlin, Germany 2Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria 3Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland 4Valiev Institute of Physics and Technology, Russian Academy of Sciences, Nakhimovskii prospekt 36/1, 117218 Moscow, Russia 5Department of Philosophy, University of Konstanz, Fach 17, 78457 Konstanz, Germany (Dated: September 18, 2020) Machine learning can help us in solving problems in the context big data analysis and classifica- tion, as well as in playing complex games such as Go. But can it also be used to find novel protocols and algorithms for applications such as large-scale quantum communication? Here we show that machine learning can be used to identify central quantum protocols, including teleportation, entan- glement purification and the quantum repeater. These schemes are of importance in long-distance quantum communication, and their discovery has shaped the field of quantum information pro- cessing. However, the usefulness of learning agents goes beyond the mere re-production of known protocols; the same approach allows one to find improved solutions to long-distance communication problems, in particular when dealing with asymmetric situations where channel noise and segment distance are non-uniform. Our findings are based on the use of projective simulation, a model of a learning agent that combines reinforcement learning and decision making in a physically motivated framework. The learning agent is provided with a universal gate set, and the desired task is specified via a reward scheme. From a technical perspective, the learning agent has to deal with stochastic environments and reactions. We utilize an idea reminiscent of hierarchical skill acquisition, where solutions to sub-problems are learned and re-used in the overall scheme. This is of particular im- portance in the development of long-distance communication schemes, and opens the way for using machine learning in the design and implementation of quantum networks. I. INTRODUCTION modern artificial intelligence [16{18]. By using projec- tive simulation (PS) [19], a physically motivated frame- work for RL, we show that teleportation, entanglement Humans have invented technologies with transform- swapping, and entanglement purification are found by a ing impact on society. One such example is the inter- PS agent. We equip the agent with a universal gate set, net, which significantly influences our everyday life. The and specify the desired task via a reward scheme. With quantum internet [1,2] could become the next genera- certain specifications of the structure of the action and tion of such a world-spanning network, and promises ap- percept spaces, RL then leads to the re-discovery of the plications that go beyond its classical counterpart. This desired protocols. Based on these elementary schemes, includes e.g. distributed quantum computation, secure we then show that such an artificial agent can also learn communication or distributed quantum sensing. Quan- more complex tasks and discover long-distance commu- tum technologies are now at the brink of being com- nication protocols, the so-called quantum repeaters [12]. mercially used, and the quantum internet is conceived The usage of elementary protocols learned previously is of as one of the key applications in this context. Such central importance in this case. We also equip the agent quantum technologies are based on the invention of a with the possibility to call sub-agents, thereby allowing number of central protocols and schemes, for instance for a design of a hierarchical scheme [20, 21] that offers quantum cryptography [3{7] and teleportation [8]. Ad- the flexibility to deal with various environmental situa- ditional schemes that solve fundamental problems such as arXiv:1904.10797v2 [quant-ph] 17 Sep 2020 tions. The proper combination of optimized block actions the accumulation of channel noise and decoherence have discovered by the sub-agents is the central element at been discovered and have also shaped future research. this learning stage, which allows the agent to find a scal- This includes e.g. entanglement purification [9{11] and able, efficient scheme for long-distance communication. the quantum repeater [12] that allow for scalable long- We are aware that we make use of existing knowledge distance quantum communication. These schemes are in the specific design of the challenges. Rediscovering considered key results whose discovery represent break- existing protocols under such guidance is naturally very throughs in the field of quantum information processing. different from the original achievement (by humans) of But to what extent are human minds required to find conceiving of and proposing them in the first place, an such schemes? essential part of which includes the identification of rele- Here we show that many of these central quantum pro- vant concepts and resources. However, the agent does not tocols can in fact be found using machine learning by only re-discover known protocols and schemes, but can phrasing the problem in a reinforcement learning (RL) go beyond known solutions. In particular, we find that in framework [13{15], the framework at the forefront of asymmetric situations, where channel noise and decoher- 2 ence are non-uniform, the schemes found by the agent II. PROJECTIVE SIMULATION FOR outperform human-designed schemes that are based on QUANTUM COMMUNICATION TASKS known solutions for symmetric cases. In this paper the process of designing quantum commu- From a technical perspective, the agent is situated in nication protocols is viewed as a reinforcement learning stochastic environments [13, 14, 22], as measurements (RL) problem. RL, and more generally machine learn- with random outcomes are central elements of some of ing (ML), is becoming increasingly more useful in au- the schemes considered. This requires to learn proper re- tomation of problem-solving in quantum information sci- actions to all measurement outcomes, e.g., the required ence [25{27]. First, ML has been shown to be capable of correction operations in a teleportation protocol depend- designing new quantum experiments [24, 28{30] and new ing on outcomes of (Bell) measurements. Additional ele- quantum algorithms [31, 32]. Next, by bridging knowl- ments are abort operations, as not all measurement out- edge about quantum algorithms with actual near-term comes lead to a situation where the resulting state can experimental capabilities, ML can be used to identify be further used. This happens for instance in entangle- problems in which quantum advantage over a classical ap- ment purification, where the process needs to be restarted proach can be obtained [33{35]. Then, ML is used to re- in some cases as the resulting state is no longer entan- alize these algorithms and protocols in quantum devices, gled. The overall scheme is thus probabilistic. These by autonomously learning how to control [36{38], error- are new challenges that have not been treated in pro- correct [39{42], and measure quantum devices [43]. Fi- jective simulation before, but the PS agent can in fact nally, given experimental data, ML can reconstruct quan- deal with such challenges. Another interesting element tum states of physical systems [44{46], learn a compact is the usage of block actions that have been learned representation of these states and characterize them [47{ previously. This is a mechanism similar to hierarchical 49]. skill learning in robotics [20, 21], and to clip composi- Here we propose learning quantum communication tion in PS [19, 23, 24], where previously learned tasks protocols by a trial and error process. This process is are used to solve more complex challenges and problems. visualized in Fig.1 as an interaction between an RL Here we use this concept for long-distance communica- agent and its environment: by trial and error the agent tion schemes. The initial situation is a quantum chan- is manipulating quantum states hence constructing com- nel that has been subdivided by multiple repeater sta- munication protocols. At each interaction step the RL tions that share entangled pairs with their neighboring agent perceives the current state of the protocol (envi- stations. Previously learned protocols, namely entangle- ronment) and chooses one of the available operations (ac- ment swapping and entanglement purification, are used tions). This action modifies the previous version of the as new primitives. Additionally, the agent is allowed to protocol and the interaction step ends. In addition to employ sub-agents that operate in the same way but deal the state of the protocol the agent gets feedback at each with a problem at a smaller scale, i.e. they find optimized interaction step. This feedback is specified by a reward block actions for shorter distances that the main agent function, which depends on the specific quantum com- can employ at the larger scale. This allows the agent munication task a)-d) in Fig.1. A reward is interpreted to deal with big systems, and re-discover the quantum by the RL agent and its memory is updated. repeater with its favorable scaling. The ability to del- The described RL approach is used for two reasons. egate is of special importance in asymmetric situations First, there is a similarity between a target quantum com- as such block actions need to be learned separately for munication protocol and a typical RL target. A target different initial states of the environment { in our case quantum communication protocol is a sequence of ele- the fidelity of the elementary pairs might vary drastically mentary operations leading to a desired quantum state, either because they correspond to segments with differ- whereas a target of an RL agent is a sequence of actions ent channel noise, or they are of different length.
Load more

Recommended publications
  • Unconditional Quantum Teleportation
    R ESEARCH A RTICLES our experiment achieves Fexp 5 0.58 6 0.02 for the field emerging from Bob’s station, thus Unconditional Quantum demonstrating the nonclassical character of this experimental implementation. Teleportation To describe the infinite-dimensional states of optical fields, it is convenient to introduce a A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, pair (x, p) of continuous variables of the electric H. J. Kimble,* E. S. Polzik field, called the quadrature-phase amplitudes (QAs), that are analogous to the canonically Quantum teleportation of optical coherent states was demonstrated experi- conjugate variables of position and momentum mentally using squeezed-state entanglement. The quantum nature of the of a massive particle (15). In terms of this achieved teleportation was verified by the experimentally determined fidelity analogy, the entangled beams shared by Alice Fexp 5 0.58 6 0.02, which describes the match between input and output states. and Bob have nonlocal correlations similar to A fidelity greater than 0.5 is not possible for coherent states without the use those first described by Einstein et al.(16). The of entanglement. This is the first realization of unconditional quantum tele- requisite EPR state is efficiently generated via portation where every state entering the device is actually teleported. the nonlinear optical process of parametric down-conversion previously demonstrated in Quantum teleportation is the disembodied subsystems of infinite-dimensional systems (17). The resulting state corresponds to a transport of an unknown quantum state from where the above advantages can be put to use. squeezed two-mode optical field.
    [Show full text]
  • Quantum Error Modelling and Correction in Long Distance Teleportation Using Singlet States by Joe Aung
    Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2002 @ Massachusetts Institute of Technology 2002. All rights reserved. Author ................... " Department of Electrical Engineering and Computer Science May 21, 2002 72-1 14 Certified by.................. .V. ..... ..'P . .. ........ Jeffrey H. Shapiro Ju us . tn Professor of Electrical Engineering Director, Research Laboratory for Electronics Thesis Supervisor Accepted by................I................... ................... Arthur C. Smith Chairman, Department Committee on Graduate Students BARKER MASSACHUSE1TS INSTITUTE OF TECHNOLOGY JUL 3 1 2002 LIBRARIES 2 Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science on May 21, 2002, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Under a multidisciplinary university research initiative (MURI) program, researchers at the Massachusetts Institute of Technology (MIT) and Northwestern University (NU) are devel- oping a long-distance, high-fidelity quantum teleportation system. This system uses a novel ultrabright source of entangled photon pairs and trapped-atom quantum memories. This thesis will investigate the potential teleportation errors involved in the MIT/NU system. A single-photon, Bell-diagonal error model is developed that allows us to restrict possible errors to just four distinct events. The effects of these errors on teleportation, as well as their probabilities of occurrence, are determined.
    [Show full text]
  • Bidirectional Quantum Controlled Teleportation by Using Five-Qubit Entangled State As a Quantum Channel
    Bidirectional Quantum Controlled Teleportation by Using Five-qubit Entangled State as a Quantum Channel Moein Sarvaghad-Moghaddam1,*, Ahmed Farouk2, Hussein Abulkasim3 to each other simultaneously. Unfortunately, the proposed Abstract— In this paper, a novel protocol is proposed for protocol required additional quantum and classical resources so implementing BQCT by using five-qubit entangled states as a that the users required two-qubit measurements and applying quantum channel which in the same time, the communicated users global unitary operations. There are many approaches and can teleport each one-qubit state to each other under permission prototypes for the exploitation of quantum principles to secure of controller. The proposed protocol depends on the Controlled- the communication between two parties and multi-parties [18, NOT operation, proper single-qubit unitary operations and single- 19, 20, 21, 22]. While these approaches used different qubit measurement in the Z-basis and X-basis. The results showed that the protocol is more efficient from the perspective such as techniques for achieving a private communication among lower shared qubits and, single qubit measurements compared to authorized users, but most of them depend on the generation of the previous work. Furthermore, the probability of obtaining secret random keys [23, 2]. In this paper, a novel protocol is Charlie’s qubit by eavesdropper is reduced, and supervisor can proposed for implementing BQCT by using five-qubit control one of the users or every two users. Also, we present a new entanglement state as a quantum channel. In this protocol, users method for transmitting n and m-qubits entangled states between may transmit an unknown one-qubit quantum state to each other Alice and Bob using proposed protocol.
    [Show full text]
  • Arxiv:2009.07590V2 [Quant-Ph] 9 Dec 2020
    Emulating quantum teleportation of a Majorana zero mode qubit He-Liang Huang,1, 2, 3 Marek Naro˙zniak,4, 5 Futian Liang,1, 2, 3 Youwei Zhao,1, 2, 3 Anthony D. Castellano,1, 2, 3 Ming Gong,1, 2, 3 Yulin Wu,1, 2, 3 Shiyu Wang,1, 2, 3 Jin Lin,1, 2, 3 Yu Xu,1, 2, 3 Hui Deng,1, 2, 3 Hao Rong,1, 2, 3 6, 7, 8 1, 2, 3 4, 8, 9, 5 1, 2, 3, 1, 2, 3 Jonathan P. Dowling ∗, Cheng-Zhi Peng, Tim Byrnes, Xiaobo Zhu, † and Jian-Wei Pan 1Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China 2Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China 3Shanghai Research Center for Quantum Sciences, Shanghai 201315, China 4New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China 5Department of Physics, New York University, New York, NY 10003, USA 6Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA 7Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 8NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China 9State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China (Dated: December 10, 2020) Topological quantum computation based on anyons is a promising approach to achieve fault- tolerant quantum computing.
    [Show full text]
  • Quantum Technology: Advances and Trends
    American Journal of Engineering and Applied Sciences Review Quantum Technology: Advances and Trends 1Lidong Wang and 2Cheryl Ann Alexander 1Institute for Systems Engineering Research, Mississippi State University, Vicksburg, Mississippi, USA 2Institute for IT innovation and Smart Health, Vicksburg, Mississippi, USA Article history Abstract: Quantum science and quantum technology have become Received: 30-03-2020 significant areas that have the potential to bring up revolutions in various Revised: 23-04-2020 branches or applications including aeronautics and astronautics, military Accepted: 13-05-2020 and defense, meteorology, brain science, healthcare, advanced manufacturing, cybersecurity, artificial intelligence, etc. In this study, we Corresponding Author: Cheryl Ann Alexander present the advances and trends of quantum technology. Specifically, the Institute for IT innovation and advances and trends cover quantum computers and Quantum Processing Smart Health, Vicksburg, Units (QPUs), quantum computation and quantum machine learning, Mississippi, USA quantum network, Quantum Key Distribution (QKD), quantum Email: [email protected] teleportation and quantum satellites, quantum measurement and quantum sensing, and post-quantum blockchain and quantum blockchain. Some challenges are also introduced. Keywords: Quantum Computer, Quantum Machine Learning, Quantum Network, Quantum Key Distribution, Quantum Teleportation, Quantum Satellite, Quantum Blockchain Introduction information and the computation that is executed throughout a transaction (Humble, 2018). The Tokyo QKD metropolitan area network was There have been advances in developing quantum established in Japan in 2015 through intercontinental equipment, which has been indicated by the number of cooperation. A 650 km QKD network was established successful QKD demonstrations. However, many problems between Washington and Ohio in the USA in 2016; a still need to be fixed though achievements of QKD have plan of a 10000 km QKD backbone network was been showcased.
    [Show full text]
  • Deterministic Quantum Teleportation Received 18 February; Accepted 26 April 2004; Doi:10.1038/Nature02600
    letters to nature Mars concretion systems. Although the analogue is not a perfect 24. Hoffman, N. White Mars: A new model for Mars’ surface and atmosphere based on CO2. Icarus 146, match in every geologic parameter, the mere presence of these 326–342 (2000). 25. Ferna´ndez-Remolar, D. et al. The Tinto River, an extreme acidic environment under control of iron, as spherical haematite concretions implies significant pore volumes of an analog of the Terra Meridiani hematite site of Mars. Planet. Space Sci. 53, 239–248 (2004). moving subsurface fluids through porous rock. Haematite is one of the few minerals found on Mars that can be Acknowledgements We thank the donors of the American Chemical Society Petroleum Research linked directly to water-related processes. Utah haematite concre- Fund, and the Bureau of Land Management-Grand Staircase Escalante National Monument for partial support of this research (to M.A.C. and W.T.P.). The work by J.O. was supported by the tions are similar to the Mars concretions with spherical mor- Spanish Ministry for Science and Technology and the Ramon y Cajal Program. The work by G.K. phology, haematite composition, and loose, weathered was supported by funding from the Italian Space Agency. accumulations. The abundance of quartz in the Utah example could pose challenges for finding spectral matches to the concre- Competing interests statement The authors declare that they have no competing financial tions. However, the similarities and differences of the Utah and interests. Mars haematite concretions should stimulate further investigations. Correspondence and requests for materials should be addressed to M.A.C.
    [Show full text]
  • Arxiv:2009.06242V1 [Quant-Ph] 14 Sep 2020 Special Type of Highly Entangled State
    Quantum teleportation of physical qubits into logical code-spaces Yi-Han Luo,1, 2, ∗ Ming-Cheng Chen,1, 2, ∗ Manuel Erhard,3, 4 Han-Sen Zhong,1, 2 Dian Wu,1, 2 Hao-Yang Tang,1, 2 Qi Zhao,1, 2 Xi-Lin Wang,1, 2 Keisuke Fujii,5 Li Li,1, 2 Nai-Le Liu,1, 2 Kae Nemoto,6, 7 William J. Munro,6, 7 Chao-Yang Lu,1, 2 Anton Zeilinger,3, 4 and Jian-Wei Pan1, 2 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China 2CAS Centre for Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China 3Austrian Academy of Sciences, Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse 3, A-1090 Vienna, Austria 4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria 5Graduate School of Engineering Science Division of Advanced Electronics and Optical Science Quantum Computing Group, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531 6NTT Basic Research Laboratories & NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan 7National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan Quantum error correction is an essential tool for reliably performing tasks for processing quantum informa- tion on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that non-transverse operations, which are essential for universal quantum computation, lead to the spread of errors.
    [Show full text]
  • Quantum Teleportation of Single-Electron States
    PHYSICAL REVIEW B 101, 195403 (2020) Quantum teleportation of single-electron states Edvin Olofsson ,1 Peter Samuelsson,1 Nicolas Brunner,2 and Patrick P. Potts 1 1Physics Department and NanoLund, Lund University, Box 118, 22100 Lund, Sweden 2Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland (Received 21 February 2020; accepted 30 March 2020; published 4 May 2020) We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations, we take into account environmental effects. DOI: 10.1103/PhysRevB.101.195403 I. INTRODUCTION systems, a field referred to as electron quantum optics [22–27], we propose a scheme for performing quantum tele- Quantum teleportation was introduced by Bennett et al. portation of single-electron states. The scheme is based on in 1993 [1] and the first experimental implementations, us- electronic analogs of optical components such as beamsplit- ing photon polarizations, started to appear in the late ’90s ters and phase shifters to manipulate electrons in a dual-rail [2,3].
    [Show full text]
  • Quantum Cryptography and Quantum Entanglement for Engineering Applications
    Quantum Cryptography and Quantum Entanglement for Engineering Applications Quantum Robotics and Autonomy ETM 4990 Mechatronics Dr. Farbod Khoshnoud Electromechanical Engineering Technology Department, College of Engineering, California State Polytechnic University, Pomona 1 Quantum Engineering • Experimental Quantum Entanglement • Experimental Quantum Cryptography • Quantum technologies for robotics and autonomy applications 2 Mechanical Systems + Classical Computers Mechanical Systems + Classical Computers/Technologies = The State of the art 3 Mechanical Systems + Quantum Technologies Mechanical Systems + Quantum Computers/Technologies = Quantum Robotics and Autonomy (e.g., The Alice and Bob Robots) 4 Literature review (Mechanical Systems and/or Education + Quantum Technologies) • Drone-to-Drone Quantum Key distribution (Kwiat, P., et al., 2017). The aim is to enhance quantum capability (not mechanical systems). • Space and underwater Quantum Communications (various references). The aim is enhancing communication not mechanical systems. • Preparing for the quantum revolution -- what is the role of higher education? (https://arxiv.org/abs/2006.16444) • Achieving a quantum smart workforce (https://arxiv.org/abs/2010.13778). 5 Introduction • When quantum technologies/computers become available in a multi-agent robotic system: How the quantum computer is integrated to mechanical systems (e.g., robots, autonomous systems) • Hybrid quantum-classical technologies for autonomous systems – quantum is good for solving some problems and classical
    [Show full text]
  • Quantum Teleportation in Quantum Dots System Abstract
    Quantum Teleportation in Quantum Dots System Hefeng Wang and Sabre Kais∗ Department of Chemistry and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907 Abstract We present a model of quantum teleportation protocol based on one-dimensional quantum dots system. Three quantum dots with three electrons are used to perform teleportation, the unknown qubit is encoded using one electron spin on quantum dot A, the other two dots B and C are coupled to form a mixed space-spin entangled state. By choosing the Hamiltonian for the mixed space- spin entangled system, we can filter the space (spin) entanglement to obtain pure spin (space) entanglement, and after a Bell measurement, the unknown qubit is transfered to quantum dot B. Selecting an appropriate Hamiltonian for the quantum gate allows the spin-based information to be transformed into a charge-based information. The possibility of generalizing this model to N-electrons is discussed. The Hamiltonian to construct the CNOT gate, and the pulse sequence to realize the Hamiltonian are discussed in detail. 1 Contents I. Introduction 2 II. Entanglement 4 III. Quantum Teleportation 6 IV. Entanglement in the one-dimensional Hubbard model 9 V. Quantum teleportation in quantum dots 10 VI. Summary 17 References 20 I. INTRODUCTION The special quantum features such as superpositions, interference and entanglement, have revolutionized the field of quantum information and quantum computation. Quantum tele- portation primarily relies on quantum entanglement, which essentially implies an intriguing property that two quantum correlated systems can not be considered independent even if they are far apart. The dream of teleportation is to be able to travel by simply reappearing at some distant location.
    [Show full text]
  • Quantum Entanglement and Teleportation Brent R. Yates Physics 555B Spring 2010
    Quantum Entanglement and Teleportation Brent R. Yates Physics 555B Spring 2010 Abstract Even Einstein has to be wrong sometimes. However, when Einstein was wrong he created a 70 year debate about the strange behavior of quantum mechanics. His debate helped prove topics such as the indeterminacy of particle states, quantum entanglement, and a rather clever use of quantum entanglement known as quantum teleportation. Introduction Quantum mechanics by nature is inherently a statistical field. A particle can never be predicted with absolute certainty, only with certain probabilities of being in a particular state. Even stranger is the idea that a particle is not in any given state but rather all states at once until it is observed. Once observed a particle is then permanently fix in the observed state. Einstein was convinced that quantum mechanics was simply a statistical approximation of a more concrete and precise description of the world. In his attempts to “complete” quantum theory Einstein introduced several ideas such as local hidden variables (parameters that could not be directly seen, but affected and ultimately determined the state of a particle). He tried to use these hidden variables to solve the “problem” of entanglement and to prove that quantum particles indeed always had fixed values. Einstein was ultimately proven wrong, but he was “brilliantly wrong” (1). The disproval of Einstein’s theories ultimately lead to concrete proof of phenomena such as entanglement, and entanglement was then exploited to allow the teleportation of quantum particles. Theoretical Entanglement The basic idea of quantum entanglement is two or more “entangled” particles have direct influence on each other, even at a distance.
    [Show full text]
  • Entanglement and Quantum Key Distribution
    Entanglement and Quantum Key Distribution By Justin Winkler Entanglement in quantum mechanics refers to particles whose individual states cannot be written without reference to the state of other particles. Such states are said to be non-separable, and measurements of the state of one entangled particle alter the state of all entangled particles. This unusual phenomena has applications in quantum teleportation, superdense coding, and various other applications relating to quantum computing. Of some interest is how entanglement can be applied to the field of quantum cryptography, particularly quantum key distribution. Quantum key distribution (QKD) is a technique that allows for secure distribution of keys to be used for encrypting and decrypting messages. The technique of QKD was proposed by Charles H. Bennett and Gilles Brassard in 1984, describing a protocol that would come to be known as BB84 [1]. BB84 was originally described using photon polarization states; no quantum entanglement was required. BB84 requires measurement in two different orthogonal bases. Making use of the case of photon polarization, one basis is typically rectilinear, with vertical polarization at 0° and horizontally polarization at 90°, while the other basis is diagonal, with vertical polarization at 45° and horizontal polarization at 135°. Bit values can then be assigned as, for example, 0 for a vertically polarized photon and 1 for a horizontally polarized photon. To distribute a key, the distributing party, Alice, creates a random bit in a random basis, sending a photon being 1 or 0 in either the rectilinear or diagonal basis. The photon created by Alice is received by Bob, who does not know the basis Alice used.
    [Show full text]