S03: Quantum Ideas

Course home page

Course information

Textbook

- A. I. Lvovsky, Quantum Physics: An Introduction Based on Photons

Additional resources

- Video lectures on YouTube

- J. Dunningham and V. Vedral, Introductory Quantum Mechanics and Relativity

- V. Scarani, Six quantum pieces

- D. J. Griffiths, Introduction to Quantum Mechanics

- R. Shankar, Principles of Quantum Mechanics

- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information

- IBM quantum computer and tutorials

Instructor

- Prof. Alexander Lvovsky

- E-mail: Alex.Lvovsky(at)physics.ox.ac.uk

- Telephone: 01865 272275

- Office: Beecroft 1^st floor

- Office hours: By appointment

Study plan

Lecture 1

- Hilbert space postulate. Dirac notation. Polarization of light.

- Secs. 1.1, 1.2, 1.3, A.1-A.4, C.1-C.3.

- Supplementary notes Photon polarization practice, Problem 1.

Lecture 2

- Measurement postulate. Polarization measurements. Orthonormal bases.

- Secs. 1.4, A.5.

- Supplementary notes Problems 2,3.

Lecture 3

- Quantum interference and complementarity. Quantum cryptography.

- Secs. 1.5, 1.6

- Supplementary notes Problem 4. End-of-chapter Problem 1.4.

Lecture 4

- Operators in quantum mechanics. Outer products. Adjoint and self-adjoint operators.

- Secs. 1.7,1.8, A.6, A.7

- Supplementary notes Problem 5. End-of-chapter Problems 1.5-1.8.

- Supplementary notes Quantum Computing 1. Quantum Computing Exercise 1.

Lecture 5

- Quantum observables. Mean and variance. Spectral decomposition

- Secs. 1.8, 1.9.1,1.9.2, A.8.

- End-of-chapter Problems 1.10-1.11.

Lecture 6

- Commutators. The uncertainty principle.

- Secs. 1.9.3, A.9.

- End-of-chapter Problems 1.1,1.12.

Lecture 7

- Quantum evolution. Schroedinger equation.

- Secs. 1.10, A.10,A.11.

- End-of-chapter Problems 1.14, 1.15.

Lecture 8

- Tensor product spaces. Entanglement. Quantum dense coding. No-cloning theorem.

- Sec. 2.1.

- End-of-chapter Problems 2.2, 2.4.

- Supplementary notes Quantum Computing 2. Quantum Computing Exercises 2,3.

Lecture 9

- Local measurements of entangled states.

- Sec. 2.2.

- End-of-chapter Problems 2.6,2.8.

Lecture 10

- Quantum nonlocality. Einstein-Podolsky-Rosen paradox. Bell's inequality.

- Secs. 2.3.

- End-of-chapter Problems 2.10 (for |F+> only), 2.15.

- Supplementary notes Quantum Computing Exercise 4.

Lecture 11

- Von Neumann measurements. Decoherence. Interpretations of quantum mechanics. Quantum computing. Quantum teleportation. Quantum repeater.

- Secs. 2.4, 2.5, 2.6

- End-of-chapter Problems 2.13, 2.16, 2.17 (for |F+> only).

- Supplementary notes Quantum Computing Exercises 5, 6.

Lecture 12

- Review of continuous-variable quantum mechanics. Wavefunctions. De Broglie wave.

- Secs. 3.1-3.3.