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Fundamentals of quantum information / Hiroyuki Sagawa, Nobuaki Yoshida

Sagawa, Hiroyuki (författare)
Yoshida, Nobuaki (författare)
ISBN 978-981-4324-23-6
Singapore ; World Scientific, cop. 2011
Engelska xii, 254 s.
  • Bok
Innehållsförteckning Ämnesord
Stäng  
  • 1. Introduction -- 2. Mathematical realization of quantum mechanics. -- State vector -- Operator -- Time evolution of wave function -- Eigenvalue and eigenstate of Hamiltonian -- 3. Basic concepts of quantum mechanics. -- Wave function and probability interpretation -- Commutation relation and uncertainty relation -- Quantum states of spin 1/2 particles -- Quantum bit -- Angular momentum, spin and rotation -- 4. EPR pair and measurement. -- EPR pair -- Transmission of quantum states -- Einsteins's locality principle in quantum mechanics -- Measurement of two correlated particles and hidden variable theorem -- CHSH inequality -- Classical correlation vs. quantal correlation: a case of nuclear fission -- EPR experiment by photon pairs -- Four-photon GHZ states -- 5. Classical computers. -- Turing machine -- von Neumann computer -- Possibility and complexity of computation -- Arithmetic operations -- Factorization and decision of prime numbers -- Combination problems -- Computational complexity and amount of computation -- Logic gates -- Logic circuits -- Sequential circuit and memory -- 6. Quantum gates. -- Quantum gates -- Controlled-operation gates -- Quantum Turing machine -- Quantum Fourier transformation (3 bit case) -- 7. Theory of information and communication. -- Shannon entropy -- Amount of information -- Entropy -- Coding information -- Von Neumann entropy -- Transmission error in communication -- Errors and channel capacity -- Shannon's theorem -- 8. Quantum computation. -- Quantum bit and quantum register -- Deutsch-Jozsa algorithm -- Shor's factorization algorithm -- Quantum Fourier transformation with n bits -- Quantum phase estimation and order finding algorithm -- Calculation of modular exponentials -- 9. Quantum cryptography. -- Secret key cryptography -- "one-time pad" cryptography -- Public key cryptography -- Public key cryptography -- Quantum key distribution -- Non-cloning theorem -- BB84 protocol -- B92 protocol -- E92 protocol -- E91 protocol -- 10. Quantum search algorithm. -- Oracle function -- Quantum oracle -- 11. Physical devices of quantum computers. -- Nuclear magnetic resonance (NMR) computers -- Principles of NMR computers -- NMR and spin rotations -- Statistical treatment -- Experiment of quantum factorization -- Ion trap computers -- Basic principles -- Ion trap -- Computation -- Preparation of the initial states -- Reading results -- Example of quantum gate -- Quantum dot computer -- Principle --Appendix A: Basic theory of numbers. -- Congruence -- Euler's theorem (Fermat's little theorem) -- Eulid's algorithm -- Diophantus equation (Indeterminate equation) -- Chinese remainder theorem -- Continued fractions -- Appendix B: Solutions to problems.

Ämnesord

Quantum computers  (LCSH)
Quantum theory  (LCSH)

Klassifikation

QA76.889 (LCC)
004.1 (DDC)
Pua (kssb/8 (machine generated))
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