Wireless Quantum Networks, Volume 2 Quantum vs Post Quantum Security: Algorithms and Design Technology

Comprehensive description of the principles, algorithms, design technology, quantum machine learning and quantum physics in quantum computing and communications

A standalone volume moving from introductory to advanced level, Wireless Quantum Networks Volume 2 provides a step-by-step approach to the subject, with numerous design examples, replacing the classical concept of using “problems and solutions” addendums at the end of the chapters/book, interspersed throughout for students to work on.

Further reading is available in Wireless Quantum Networks Volume 1: Intelligent Continuous Variable Technology.

Sample topics covered in Wireless Quantum Networks Volume 2 include:

• Distributed quantum computing (QC), which requires quantum networks (QN) to enable connections between quantum computers
• General QC algorithms and communication, QC and artificial intelligence (quantum machine learning), quantum cyber security, quantum circuit design, and related quantum physics phenomena
• Advanced research areas in which quantum technology is becoming a part of, including communications, medicine, biotechnology, chemistry, and more
• Quantum key distribution over optical and sub optical bands (Terahertz) including wavelengths significantly lower than optical, QC reinforcement learning based protocols, satellite QN, post-quantum cryptography, qubit physics, and implementation examples
• QN optimization, Q Memories and QN Stability

Wireless Quantum Networks Volume 2 is an essential learning resource on the subject for professional computer science and communication engineers, researchers, and under/post-graduate students. It is also a useful reference for regulators in industry seeking to gain an understanding of the subject and complexities of the field.

Savo Glisic, Research Professor, Worcester Polytechnic Institute, Massachusetts, USA. Professor Glisic (Senior Member, IEEE) was a Visiting Scientist with the Cranfield Institute of  Technology, Cranfield, U.K., from 1976 to 1977, and the University of California, San  Diego, from 1986 to 1987. He is a Former Professor with the University of Oulu, Finland,  and the INS Institute for Networking Sciences/Globalcomm Oy. He has been active in the field of wireless communications for 30+ years.

Preface

QUANTUM vs POST QUANTUM SECURITY:

Algorithms and Design Technology

Ch 1 INTRODUCTION

1.1 Motivation

1.2 Structure of the book

Ch 2 CV QUANTUM KEY DISTRIBUTION

2.1 Fundamentals of CVQKD

2.1.1 Security of CVQKD protocols

2.2 Composable security proof for cv QKD

2.2.1 Security Proof Overview

2.2.2. Quantum Key Distribution and Composable Security

2.2.3 Description of the CV QKD protocol

2.2.3.1. State Preparation

2.2.3.2. Measurement

2.2.3.3. Error correction

2.2.3.4. Parameter Estimation

2.2.3.5. Privacy Amplification

2.2.4. Expected secret key rate

2.2.5 Analytical Tools

2.2.5.1. Leftover Hash Lemma

2.2.5.2. Smooth  min⁡‐entropy of a conditional state

2.2.5.3. Lower bound on the entropy of an i.i.d. variable

2.2.5.4. Gaussian states and covariance matrices

2.2.6 Parameter Estimation in the protocol E_0

2.2.6 .1. Preliminaries

2.2.6.2. Proofs related to the analysis of Parameter Estimation

2.2.6.3. Probability of the bad event

2.2.6.4. Analysis of the Parameter Estimation

2.2.7 Security of the protocol E_0 against collective attacks

2.2.7.1 A security proof against general attacks without active symmetrization

2.3 Composable security of two-way cv QKD

2.3.1 Overview of the protocol

2.3.2 Secret key rate of the two‐way protocol

2.4 Security of cv QKD via a Gaussian de Finetti reduction

2.4.1 Generalized SU(2,2) coherent states

2.4.2 Technical lemmas

2.4.3. Finite energy version of de Finetti theorem

2.4.4 Security proof for a modified CV QKD protocol

2.4.5 Postelection technique

2.4.6 Security against collective attacks

2.4.7 Energy test

2.5 Secure Multi-party Quantum Computation

2.5.1 MPQC Basics

2.5.2 Multi‐party Quantum Computation: Definitions

2.5.3 System Model

2.5.4 Computation of Clifford and measurement

2.5.5 Protocol: MPQC for general quantum circuits

REFERENCES

Ch 3 QKD OVER SUBOPTICAL BANDS:

Towards Heterogenous Wireless & cv Quantum Networks

3.1 cv QKD with Adaptive Multicarrier Quadrature Division Modulation

3.1.1Multicarrier Quadrature Division Modulation

3.1.2 Adaptive Modulation Variance

3.1.3 Efficiency of AMQD Modulation

3.2 QKD over THz Band

3.2.1 TERAHERTZ QKD: System Model

3.2.2 System performance in the Extended Terahertz range

3.2.3 Derivation of the secret‐key rates

3.2.4 Coherent Bidirectional Terahertz‐Optical Converter

3.2.5 Implementation

3.3 Quantum cryptography at wavelengths

considerably longer than optical

3.3.1 Summary of analytical tools

REFERENCE

Ch 4  REINFORCEMENT LEARNING based QN PROTOCOLS

4.1 Quantum Network Protocols

4.1.1 Summary of the analytical tools

4.1.2 Quantum Link Layer Protocol

4.1.3 Reinforcement Learning-based quantum decision processes

4.1.4 Quantum Networks

REFERENCES

Ch 5 QN STABILITY

5.1 Dynamic QN PROTOCOLS

5.1.1 Dynamic random subgraphs

5.1.2 Dynamic Quantum states

5.1.3 Quantum Decision Processes for QN Protocols

5.1.4 Performance Measures

5.1.5 Policy optimization

5.2 QN Stability

5.2.1 Stabi1ity of an entang1ed quantum network.

REFERENCES

Ch 6 SATELLITE QN

6.1 Elementary Link Generation with Satellites

6.2 Implementation Aspects of cv Satellite QN

6.2.1 Uplink/Downlink Free‐Space Optical Channels

6.2.2 CV Quantum Systems in Satellite Networks

6.2.3 Continuous Variable‐QKD in Satellite Networks

6.2.4 Entanglement and CV‐QK Distribution in Satellite Networks

6.2.5 Non-Gaussian CV Quantum Communication over Atmospheric Channels

REFERENCES

Ch 7 Q MEMORIES

7.1 System model.

7.2 Integrated Local Unitaries U_ML

7.2.1 Factorization Unitary U_ML=U_F U_CQT U_P U_CQT^†,

7.2.1.1 Unitary U_F 〖(U〗_ML=U_F U_CQT U_P U_CQT^†),

7.2.1.2 Unitary U_CQT 〖(U〗_ML=U_FU_CQTU_P U_CQT^†),

7.2.1.3 Basis partitioning unitary U_P  〖(U〗_ML=U_F U_CQT U_P U_CQT^†),

7.2.1.4 Inverse quantum constant Q transform  U_CQT^†  〖(U〗_ML=U_F U_CQT U_P U_CQT^†),

7.2.1.5 Inverse quantum DSTFT and quantum DFT

REFERENCES

Ch 8 Quantum Network Optimization

8.1 Algorithms

8.1.1 The Quantum Alternating Operator Ansatz (QAOA)

8.1.2 QAOA Mappings: Strings

8.1.2.1 Example: Max‐κ‐ColorableSubgraph

8.1.2.2 Full QAOA Mapping

8.1.3 QAOA Mappings: Orderings and Schedules

8.1.4 QAOA mappings for a variety of NP optimization problems

8.1.4.1 Bit‐Flip (X) Mixers

8.1.4.2 Controlled‐Bit‐Flip (Λ_f (X)) Mixers

8.1.4.3 Mixers

8.1.4.4 Controlled‐XY  Mixers

8.1.4.5 Permutation Mixers

8.2 Multidomain Optimization of Quantum Network

8.2.1 Quantum‐Domain Optimization (QDO)

8.2.2 Classical‐Domain Optimization (CDO)

REFERENCES

Ch 9 POST‐QUANTUM CRYPTOGRAPHY

9.1 Overview of Post-Quantum Cryptosystems

9.1.2 Lattice based cryptography

9.1.3 Hash based cryptography

9.1.4 Code based cryptography

9.2 Rainbow

9.2.1 Multivariate Public Key Cryptography

9.2.2 Rainbow Algorithm Specification

9.2.3 Key Generation Speed Up

9.2.4 Resistance to Attacks

9.3 NTRU N-th degree Truncated polynomial Ring Units

9.3.1 Specification of NTRU Cryptosystem

9.3.2 Security of NTRU

9.4 LWE Cryptosystem

9.4.1 Preliminaries

9.4.2 LWE Algorithm Variants

 9.4.3 LWE Public Key Cryptosystem

9.5 BLISS (Bimodal Lattice Signature Scheme (BLISS)

9.5.1 BLISS: A Lattice Signature Scheme using Bimodal Gaussians

9.5.2 Implementation of BLISS

9.6 Variants of Merkle Signature Scheme

9.6.1 The Winternitz One‐time Signature Scheme

9.6.2 The Merkle Signature Scheme

9.6.3 CMSS

9.7 Lamport Signature

9.7.1 Improved Lamport one‐time signature

9.8 McEllice Cryptosystem: Code-based cryptography

9.8.1 McEliece Cryptosystem Using Extended Golay Code

9.9 Niederreiter Cryptosystem

9.9.1 Niederreiter cryptosystems and Quasi‐Cyclic Codes

9.9.2 Subgroup K is indistinguishable

9.9.3 Fault Attack on the Niederreiter Cryptosystem

9.9.3.1 Binary Goppa Codes

9.9.3.2 Binary Irreducible Goppa Cryptosystems

9.9.3.3 The BIG‐N Fault Injection Framework

9.9.3.4 Constant and Quadratic Fault Injection Sequences

9.9.3.5  The BIG‐N Fault Attack

Appendix 9.1 Key Generation for a SIS‐Based Scheme

REFERENCES

Ch 10 QUANTUM CRYPTOGRAPHY

10.1 Discrete Variable Protocols

10.1.1 Prepare and measure protocols

10.1.2 Countermeasures

10.1.3 Entanglement‐based QKD

10.1.4 Two‐way quantum communication

10.2 Device‐Independent QKD

10.2.1 The link between Bell violation and unpredictability

10.2.2 Performance bounds

10.2.3 Protocols for DI‐QKD

10.2.4 Implementation of DI‐QKD protocols

10.3 Continuous‐Variable QKD

10.3.1. One‐way CV‐QKD protocols

10.3.2. Two‐way CV‐QKD protocols

10.4 Theoretical Models of Security

10.4.1 Heisenberg’s uncertainty principle

10.5 Limits of Point‐to‐Point QKD

10.5.1 Adaptive protocols and two‐way assisted capacities

10.5.2 General weak‐converse upper bound

10.5.3 LOCC simulation of quantum channels

10.5.4 Teleportation covariance and simulability

10.5.5 Strong and uniform convergence

10.5.6 Stretching of an adaptive protocol

10.5.7 Upper bound simplification for two‐way assisted capacities

10.5.8 Bounds for teleportation‐covariant channels

10.5.9 Capacities for distillable channels

10.6 QKD Against a Bounded Quantum Memory

10.6.1 Entropic uncertainty relations

10.6.2 Bounded quantum storage model

10.6.3 Quantum data locking

Appendix 10.A: Formulas for Gaussian states

Ch 11 IMPLEMENTATION EXAMPLES OF cv QKD

11.1 Effective Channel Model

11.2 Modelling Transceiver Component

11.3 Protocols

11.4. Signal‐to‐Noise Ratio

11.5 Holevo Information

11.6 Purification Attacks

11.7 Security Assumptions

11.8 Parameter Estimation

11.9 Noise Models

11.9.1 Modulation Noise

11.9.2. Phase‐Recovery Noise

11.9.3. Raman Noise

11.9.4 Common‐Mode Rejection Ratio

11.9.5 Detection Noise

11.9.6 ADC Quantization Noise

11.6. Implementation Example

11.11 QKD Implementation at Terahertz Bands

11.8.1 System Model

11.8.2 The Model of Noise and Eve’s Attack

11.8.3 Reconciliation

11.8.4 Secret Key Rate of Thz‐MCM‐CVQKD

11.2 QKD Over Optical Backbone Networks

11.6.1 Preliminaries

 11.6.2 System Model

11.6.3 Network Optimization

11.3 Quantum Receivers

11.8.1 EA Classical Optical Communication System

11.8.2 Nonlinear Receivers

11.8.3 Joint Receivers

11.8.4 System Performance

Ch 12 qubit PHYSICS

12.1 Superconducting Qubits

12.1.1 Qubit Hamiltonian engineering

12.1.2 Interaction Hamiltonian engineering

12.1.3 Qubit Control

12.1.4 Qubit Readout

12.2 Qubit gates using the spin states of coupled single-electron quantum dots

12.2.1 Analytical Model

12.3 Quantum Logic by Polarizing Beam Splitters

12.3.1 CNOT Using Four‐Photon Entangled States

12.3.2 CNOT Using Two‐Photon Entangled States

12.4 Quantum Gates Implemented by Trapped Ions

12.4.1 Collective Vibrational Motions

12.4.2 Laser‐Ion Interaction

12.4.3 Quantum Gates

12.4.4 Quantum Logic Networks

12.4.5 Speed of Quantum Gates

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