Quantum information theory
Summary
After recapping the basics of quantum theory from an information theoretic perspective, we will cover more advanced topics in quantum information theory. This includes introducing measures of quantum information, and developing a more advanced understanding quantum states, channels and measurements.
Content
An operational introduction to quantum information theory
- Classical state spaces, measurements and operations
- The quantum state spaces, quantum measurements and operations
- Multiple qubit systems, reduced states and purifications.
Quantum Measurements
- POVM Measurements
- Naimark's Dilation Theorem
- Distinguishing quantum states
- The measurement problem
- Quantifying shot noise
Quantum channels
- Definition and examples of quantum channels
- Stinespring Dilation Theorem
- Choi representation of channels
- Vectorization notation for channels (and beyond)
Measures of information
- Shannon entropy
- Shannon's noiseless coding theorem
- Von Neumann entropy
- Schumacher's quantum noiseless channel coding theorem
- Entropic inequalities
- Matrix distance measures
Entanglement Theory
- Resource theory of entanglement
- Entanglement entropy
- Witnessing entanglement
- The problem of mixed state entanglement
Learning Prerequisites
Required courses
Essential:
Quantum Physics I, Quantum Physics II
Some knowledge of the basics of quantum computing would be helpful to provide context to the topics studied here. I recommend taking this course in parallel with Vincenzo Savona's Quantum Computing Course PHYS-641 (or attending the basic introduction to quantum computing provided in QUANT-400).
It is worth nothing that in the first half of the course there will be some overlap with Jean-Philippe Brantut's Quantum Optics and Quantum Information Course PHYS-454. However, the two courses take different perspectives and so will be complementary.
Learning Outcomes
By the end of the course, the student must be able to:
- Demonstrate an advanced understanding of quantum information theory.
Assessment methods
60% Written exam, 40% assessed homework tasks.
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Quantum information theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel