Registration Deadline: January 24, 2027

Instructor: Professor Jason Crann, Carleton University

Course Dates: 
Mid-Semester Break: 
Lecture Time: 
Office Hours: 

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 

Format: 

Course Description

Continuous variable quantum information aims to encode and process information using continuous degrees of freedom, such as the quadrature amplitudes of quantum harmonic oscillators or electromagnetic fields. Its increasing experimental realization within quantum optics makes it a desirable platform for quantum computation and communication. All the while, it has a rich mathematical foundation, incorporating group theory, representation theory, symplectic liner algebra, Fourier and functional analysis. The course will introduce students to the mathematical formalism of continuous variable quantum information together with important applications such as Gaussian states and channels, homodyne detection, continuous variable gate teleportation and quantum error correction. Successful students will have the knowledge base to read current literature in continuous variable quantum information theory.

Approximate List of Topics

• Hilbert spaces: tensor products, quantum states and observables.
• Phase space: Heisenberg and symplectic groups, canonical commutation relations, metaplectic representation, Wigner and characteristic functions of quantum states.
• Gaussian states: normal mode decomposition, von Neumann entropy, purity.
• Gaussian measurements and channels: homodyne and hetreodyne detection, classical Gaussian noise, attenuation and amplification.
• Continuous variable superdense coding and gate teleportation.
• Continuous variable quantum error correction: stabilizer formalism, Gottesman-Preskill-Kitaev states, cat states.
• Continuous variable cluster states and measurement based quantum computation.

Prerequisites

Linear algebra and graduate-level analysis are essential. Knowledge of elementary quantum mechanics and/or quantum computing is an asset, but not necessary to succeed in the course.

Evaluation

Two assignments worth 15% each, and one final project worth 70% consisting of a 5-page written summary of a topic related to the course and a 15-minute virtual presentation on that topic.

Resources

• A. S. Holevo, Quantum Systems, Channels, Information. A Mathematical Introduction, De Gruyter Studies in Mathematical Physics, 16. De Gruyter, Berlin, 2012.
• A. Serafini, Quantum Continuous Variables: A Primer of Theoretical Methods. CRP Press, 2017.
• C. Weedbrook et. al., Gaussian quantum information. Reviews of Modern Physics, 84 (2) (2021), 621-669.