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Quantum optics and quantum computation : an introduction /

This book studies the application of quantum mechanics to some of the most current and notable concepts in the area, such as quantum optics, cryptography, teleportation, and computing. Written as a complete and comprehensive course text, this book works through mathematically rigorous material using...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autores principales:	Bhattacharyya, Dipankar (Professor of physics) (Autor), Guha, Jyotirmoy (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]
Colección:	IOP (Series). Release 22. IOP series in advances in optics, photonics and optoelectronics. IOP ebooks. 2022 collection.
Temas:	Quantum optics. Quantum computing. Optical physics. Optics and photonics.
Acceso en línea:	Texto completo

Tabla de Contenidos:

1. Bra ket algebra of Dirac
1.1. The bra and ket notation of Dirac
1.2. Hermitian conjugation
1.3. Definition of inner product (also called overlap)
1.4. Definition of outer product
1.5. Eigenvalue equation
1.6. Linear vector space
1.7. Linear independence
1.8. Linear dependence
1.9. Span (expansion of an arbitrary ket)/expansion postulate
1.10. Ket space, bra space, dual space
1.11. Physical significance of inner product <m|n>
1.12. Norm and the process of normalization
1.13. Ortho-normalization (orthogonal + normalized)
1.14. Orthonormal basis (orthogonal + normalized + linearly independent + span)
1.15. Expansion postulate
1.16. Projection operator
1.17. Normal matrix
1.18. Spectral theorem
1.19. Elements of a matrix in Bra Ket notation
1.20. Hermitian matrix operator
1.21. Unitary matrix
1.22. Diagonalization of a matrix--change of basis
1.23. Triangle laws (inequality and equality)
1.24. Cauchy-Schwarz laws (inequality and equality)
1.25. Commutator bracket
1.26. Trace
1.27. Pauli spin matrices
1.28. Orthogonal matrix operator
1.29. Standard method of ortho-normalization Graham-Schmidt ortho-normalization procedure
1.30. Definition of average value
1.31. Some definitions
1.32. Kroneckar product (symbol [Kronecker product]) or direct product or tensor product
1.33. Further reading
1.34. Problems
2. Postulates of quantum mechanics
2.1. First postulate : observables are replaced by operators
2.2. Second postulate : state vector and wave function
2.3. Third postulate : process of measurement
2.4. Fourth postulate : Time evolution of a state
2.5. Solution of the Schrödinger equation
2.6. Unitary operator keeps the length of state vector constant
2.7. Heisenberg's uncertainty principle or principle of indeterminism
2.8. Further reading
2.9. Problems
3. Introduction to quantum computing
3.1. Introduction
3.2. Some basic ideas about classical and quantum computing
3.3. Definition of certain terms relating to quantum computing
3.4. Journey towards quantum computing
3.5. Need for quantum computers
3.6. Landauer's principle
3.7. Quantum computing
3.8. Bits 0 and 1
3.9. A bit of Boolean algebra
3.10. Gate
3.11. Computational complexity
3.12. Further reading
3.13. Problems
4. Quantum bits
4.1. Qubits and comparison with classical bits
4.2. Qubit model applied to the Stern-Gerlach experiment
4.3. Qubit model applied to polarized photon (computational and Hadamard basis introduced)
4.4. Bloch sphere representation of a qubit
4.5. Multiple qubits
4.6. Explicit representation of the basis states
4.7. Bell state or EPR pair (or state)
4.8. Global phase and relative phase
4.9. Measurement depends on choice of basis
4.10. Further reading
4.11. Problems
5. Quantum circuits
5.1. Quantum gate and quantum circuit
5.2. Single-qubit gates
5.3. Quantum NOT gate or Pauli X̂ gate ([̂sigma]x)
5.4. Ẑ gate or Pauli Ẑ gate ([̂sigma]z)
5.5. Pauli Ŷ gate or [̂sigma]y
5.6. Phase shift gates (P̂ gate, Ŝ gate, T̂ gate)
5.7. Hadamard gate Ĥ, Hadamard basis |+>, | - >
5.8. Unitary matrix as length preserving matrix
5.9. Rotation gates R̂X([theta]), R̂Y([theta]), R̂Z([theta])
5.10. Multi-qubit gates
5.11. Controlled-NOT gate or CNOT gate
5.12. Preparing Bell states
5.13. Swap gate
5.14. Controlled U gates
5.15. Toffoli quantum gate or CCNOT gate (controlled controlled NOT gate)
5.16. Controlled SWAP gate or CS gate or Fredkin gate
5.17. Deutsch gate
5.18. Implementing classical computation by quantum gates
5.19. Plan of a quantum circuit
5.20. Quantum half adder circuit
5.21. Quantum full adder circuit
5.22. Oracle (black box) in quantum computer
5.23. Hadamard transformation on each of n qubits leads to a linear superposition of 2n states
5.24. Process of measurement
5.25. Quantum coin flipping
5.26. Further reading
5.27. Problems
6. Teleportation and super dense coding
6.1. Quantum no-cloning theorem
6.2. Teleportation
6.3. Super dense coding (or dense coding) (of Bennett and Wiesner)
6.4. Further reading
6.5. Problems
7. Pure and mixed state
7.1. Pure state
7.2. Mixed state
7.3. Density operator (introduced by Von Neumann)
7.4. Density operator for a pure state
7.5. Average
7.6. Density operator of a mixed state (or an ensemble)
7.7. Quantum mechanics of an ensemble
7.8. Density matrix for a two-level spin system (Stern-Gerlach experiment)
7.9. Single-qubit density operator in terms of Pauli matrices
7.10. Some illustration of density matrix for pure and mixed states
7.11. Partially mixed, completely mixed, maximally mixed states
7.12. Time evolution of density matrix : Liouville-Von Neumann equation
7.13. Partial trace and the reduced density matrix
7.14. Measurement theory of mixed states
7.15. Positive operator valued measure (POVM)
7.16. Further reading
7.17. Problems
8. Quantum algorithms
8.1. Quantum parallelism
8.2. Reversibility
8.3. XOR is addition modulo 2
8.4. Quantum arithmetic and function evaluations
8.5. Deutsch algorithm
8.6. Deutsch-Jozsa (DJ) algorithm
8.7. Bernstein-Vazirani algorithm
8.8. Simon algorithm
8.9. Grover's search algorithm
8.10. Discrete integral transform
8.11. Quantum Fourier transform
8.12. Finding period using QFT
8.13. Implementation of QFT
8.14. Some definitions and GCD evaluation
8.15. Inverse modulo
8.16. Shor's algorithm
8.17. Further reading
8.18. Problems
9. Quantum error correction
9.1. Error in classical computing
9.2. Errors in quantum computing/communication
9.3. The phase flip
9.4. Qubit transmission from Alice to Bob
9.5. Converting a phase flip error to qubit flip error
9.6. Shor's nine-qubit error code
9.7. Further reading
9.8. Problems
10. Quantum information
10.1. Classical information theory
10.2. Decision tree
10.3. Measure of information : Shannon's entropy
10.4. Statistical entropy and Shannon's information entropy
10.5. Communication system
10.6. Shannon's noiseless coding theorem
10.7. Prefix code, binary tree
10.8. Quantum information theory, Von Neumann entropy
10.9. Further reading
10.10. Problems
11. EPR paradox and Bell inequalities
11.1. EPR paradox
11.2. David Bohm's version of EPR paradox (1951)
11.3. Bell's (Gedanken) experiment : EPR and Bell's inequalities
11.4. Clauser, Horne, Shimony and Holt's inequality
11.5. Further reading
11.6. Problems
12. Cryptography--the art of coding
12.1. A bit of history of cryptography
12.2. Essential elements of cryptography
12.3. One-time pad
12.4. RSA cryptosystem
12.5. Fermat's little theorem
12.6. Euler theorem
12.7. Chinese remainder theorem
12.8. RSA algorithm
12.9. Quantum cryptography
12.10. Protocol of quantum cryptography
12.11. Further reading
12.12. Problems
13. Experimental aspects of quantum computing
13.1. Basic principle of nuclear magnetic resonance quantum computing
13.2. Further reading
14. Light-matter interactions
14.1. Interaction Hamiltonian
14.2. Rabi oscillations
14.3. Weak field case
14.4. Strong field case : Rabi oscillations
14.5. Damping phenomena
14.6. The density matrix
14.7. Pure and mixed states
14.8. Equation of motion of the density operator
14.9. Inclusion of decay phenomena
14.10. Vector model of density matrix equations of motion
14.11. Power broadening and saturation of the spectrum
14.12. Spectral line broadening mechanism
14.13. Natural broadening
14.14. Collision or pressure broadening
14.15. Inhomogeneous broadening or Doppler broadening
14.16. Further reading
14.17. Problems
15. Laser spectroscopy and atomic coherence
15.1. Moving two-level atoms in a travelling wave field
15.2. Moving atoms in a standing wave
15.3. Lamb dip
15.4. Crossover resonances
15.5. Atomic coherence phenomena
15.6. EIT Hamiltonian of the system
15.7. Dressed states picture
15.8. Coherent population trapping
15.9. Electromagnetically induced absorption (EIA)
15.10. Further reading
15.11. Problems
16. Quantum theory of radiation
16.1. Maxwell's equations
16.2. The electromagnetic field in a cavity
16.3. Quantization of a single mode
16.4. Multimode radiation field
16.5. Coherent states
16.6. Squeezed states of light
16.7. Further reading
16.8. Problems
17. Interaction of an atom with a quantized field
17.1. Interaction Hamiltonian in terms of Pauli operators
17.2. Absorption and emission phenomena
17.3. Dressed states
17.4. Jaynes-Cummings model
17.5. Theory of spontaneous emission : Wigner-Weisskopf model
17.6. Further reading
17.7. Problems
18. Photon statistics
18.1. Young's double-slit experiment
18.2. Hanbury Brown-Twiss experiment
18.3. Photon counter
18.4. Outcome of the photon counter
18.5. Photon statistics of a perfectly coherent light
18.6. Photon statistics of a thermal light
18.7. Classification of light by second-order correlation function and photon statistics.
18.8. Photon bunching and anti-bunching
18.9. Further reading
18.10. Problems.

Quantum optics and quantum computation : an introduction /

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