Quantum Cryptography and Quantum Entanglement for Engineering Applications
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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. -
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. -
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. -
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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. -
Quantum Computing Methods for Supervised Learning Arxiv
Quantum Computing Methods for Supervised Learning Viraj Kulkarni1, Milind Kulkarni1, Aniruddha Pant2 1 Vishwakarma University 2 DeepTek Inc June 23, 2020 Abstract The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon semiconductor miniaturization approaches its physics limits, quantum computing is increasingly being considered to cater to these computational needs in the future. Small-scale quantum computers and quantum annealers have been built and are already being sold commercially. Quantum computers can benefit machine learning research and application across all science and engineering domains. However, owing to its roots in quantum mechanics, research in this field has so far been confined within the purview of the physics community, and most work is not easily accessible to researchers from other disciplines. In this paper, we provide a background and summarize key results of quantum computing before exploring its application to supervised machine learning problems. By eschewing results from physics that have little bearing on quantum computation, we hope to make this introduction accessible to data scientists, machine learning practitioners, and researchers from across disciplines. 1 Introduction Supervised learning is the most commonly applied form of machine learning. It works in two arXiv:2006.12025v1 [quant-ph] 22 Jun 2020 stages. During the training stage, the algorithm extracts patterns from the training dataset that contains pairs of samples and labels and converts these patterns into a mathematical representation called a model. During the inference stage, this model is used to make predictions about unseen samples. -
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. -
Quantum Information Science
Quantum Information Science Seth Lloyd Professor of Quantum-Mechanical Engineering Director, WM Keck Center for Extreme Quantum Information Theory (xQIT) Massachusetts Institute of Technology Article Outline: Glossary I. Definition of the Subject and Its Importance II. Introduction III. Quantum Mechanics IV. Quantum Computation V. Noise and Errors VI. Quantum Communication VII. Implications and Conclusions 1 Glossary Algorithm: A systematic procedure for solving a problem, frequently implemented as a computer program. Bit: The fundamental unit of information, representing the distinction between two possi- ble states, conventionally called 0 and 1. The word ‘bit’ is also used to refer to a physical system that registers a bit of information. Boolean Algebra: The mathematics of manipulating bits using simple operations such as AND, OR, NOT, and COPY. Communication Channel: A physical system that allows information to be transmitted from one place to another. Computer: A device for processing information. A digital computer uses Boolean algebra (q.v.) to processes information in the form of bits. Cryptography: The science and technique of encoding information in a secret form. The process of encoding is called encryption, and a system for encoding and decoding is called a cipher. A key is a piece of information used for encoding or decoding. Public-key cryptography operates using a public key by which information is encrypted, and a separate private key by which the encrypted message is decoded. Decoherence: A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers and quantum communication channels. -
Scalable Quantum Cryptography Network for Protected Automation Communication Making Quantum Key Distribution (QKD) Available to Critical Energy Infrastructure
Scalable Quantum Cryptography Network for Protected Automation Communication Making quantum key distribution (QKD) available to critical energy infrastructure Background changes the key in an immediate and Benefits measurable way, reducing the risk that The power grid is increasingly more reliant information thought to be securely • QKD lets the operator know, in real- on a distributed network of automation encrypted has actually been compromised. time, if a secret key has been stolen components such as phasor measurement units (PMUs) and supervisory control and Objectives • Reduces the risk that a “man-in-the- data acquisition (SCADA) systems, to middle” cyber-attack might allow In the past, QKD solutions have been unauthorized access to energy manage the generation, transmission and limited to point-to-point communications sector data distribution of electricity. As the number only. To network many devices required of deployed components has grown dedicated QKD systems to be established Partners rapidly, so too has the need for between every client on the network. This accompanying cybersecurity measures that resulted in an expensive and complex • Qubitekk, Inc. (lead) enable the grid to sustain critical functions network of multiple QKD links. To • Oak Ridge National Laboratory even during a cyber-attack. To protect achieve multi-client communications over (ORNL) against cyber-attacks, many aspects of a single quantum channel, Oak Ridge cybersecurity must be addressed in • Schweitzer Engineering Laboratories National Laboratory (ORNL) developed a parallel. However, authentication and cost-effective solution that combined • EPB encryption of data communication between commercial point-to-point QKD systems • University of Tennessee distributed automation components is of with a new, innovative add-on technology particular importance to ensure resilient called Accessible QKD for Cost-Effective energy delivery systems. -
Quantum Error Correcting Codes and the Security Proof of the BB84 Protocol
Quantum Error Correcting Codes and the Security Proof of the BB84 Protocol Ramesh Bhandari Laboratory for Telecommunication Sciences 8080 Greenmead Drive, College Park, Maryland 20740, USA [email protected] (Dated: December 2011) We describe the popular BB84 protocol and critically examine its security proof as presented by Shor and Preskill. The proof requires the use of quantum error-correcting codes called the Calderbank-Shor- Steanne (CSS) quantum codes. These quantum codes are constructed in the quantum domain from two suitable classical linear codes, one used to correct for bit-flip errors and the other for phase-flip errors. Consequently, as a prelude to the security proof, the report reviews the essential properties of linear codes, especially the concept of cosets, before building the quantum codes that are utilized in the proof. The proof considers a security entanglement-based protocol, which is subsequently reduced to a “Prepare and Measure” protocol similar in structure to the BB84 protocol, thus establishing the security of the BB84 protocol. The proof, however, is not without assumptions, which are also enumerated. The treatment throughout is pedagogical, and this report, therefore, serves as a useful tutorial for researchers, practitioners and students, new to the field of quantum information science, in particular quantum cryptography, as it develops the proof in a systematic manner, starting from the properties of linear codes, and then advancing to the quantum error-correcting codes, which are critical to the understanding -
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. -
A Cryptographic Leash on Quantum Devices
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 57, Number 1, January 2020, Pages 39–76 https://doi.org/10.1090/bull/1678 Article electronically published on October 9, 2019 VERIFYING QUANTUM COMPUTATIONS AT SCALE: A CRYPTOGRAPHIC LEASH ON QUANTUM DEVICES THOMAS VIDICK Abstract. Rapid technological advances point to a near future where engi- neered devices based on the laws of quantum mechanics are able to implement computations that can no longer be emulated on a classical computer. Once that stage is reached, will it be possible to verify the results of the quantum device? Recently, Mahadev introduced a solution to the following problem: Is it possible to delegate a quantum computation to a quantum device in a way that the final outcome of the computation can be verified on a classical computer, given that the device may be faulty or adversarial and given only the ability to generate classical instructions and obtain classical readout information in return? Mahadev’s solution combines the framework of interactive proof systems from complexity theory with an ingenious use of classical cryptographic tech- niques to tie a “cryptographic leash” around the quantum device. In these notes I give a self-contained introduction to her elegant solution, explaining the required concepts from complexity, quantum computing, and cryptogra- phy, and how they are brought together in Mahadev’s protocol for classical verification of quantum computations. Quantum mechanics has been a source of endless fascination throughout the 20th century—and continues to be in the 21st. Two of the most thought-provoking as- pects of the theory are the exponential scaling of parameter space (a pure state of n qubits requires 2n −1 complex parameters to be fully specified), and the uncertainty principle (measurements represented by noncommuting observables cannot be per- formed simultaneously without perturbing the state). -
Foundations of Quantum Computing and Complexity
Foundations of quantum computing and complexity Richard Jozsa DAMTP University of CamBridge Why quantum computing? - physics and computation A key question: what is computation.. ..fundamentally? What makes it work? What determines its limitations?... Information storage bits 0,1 -- not abstract Boolean values but two distinguishable states of a physical system Information processing: updating information A physical evolution of the information-carrying physical system Hence (Deutsch 1985): Possibilities and limitations of information storage / processing / communication must all depend on the Laws of Physics and cannot be determined from mathematics alone! Conventional computation (bits / Boolean operations etc.) based on structures from classical physics. But classical physics has been superseded by quantum physics … Current very high interest in Quantum Computing “Quantum supremacy” expectation of imminent availability of a QC device that can perform some (albeit maybe not at all useful..) computational tasK beyond the capability of all currently existing classical computers. More generally: many other applications of quantum computing and quantum information ideas: Novel possibilities for information security (quantum cryptography), communication (teleportation, quantum channels), ultra-high precision sensing, etc; and with larger QC devices: “useful” computational tasKs (quantum algorithms offering significant benefits over possibilities of classical computing) such as: Factoring and discrete logs evaluation; Simulation of quantum systems: design of large molecules (quantum chemistry) for new nano-materials, drugs etc. Some Kinds of optimisation tasKs (semi-definite programming etc), search problems. Currently: we’re on the cusp of a “quantum revolution in technology”. Novel quantum effects for computation and complexity Quantum entanglement; Superposition/interference; Quantum measurement. Quantum processes cannot compute anything that’s not computable classically.