Quantum information theory

PHYS-550 / 4 credits

Teacher: Holmes Zoë

Language: English

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
  • State tomography
  • The measurement problem
  • Quantifying shot noise

Quantum channels

  • Definition and examples of quantum channels
  • Stinespring Dilation Theorem
  • Choi representation of channels
  • Channel tomography

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

Highly beneficial:

Some knowledge of the basics of quantum computing will be assumed. Therefore this course would follow on nicely from Vincenzo Savona's Quantum Computing Course PHYS-641. Alternatively, the basic introduction to quantum computing provided in QUANT-400 would suffice.

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 will 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.

Teaching methods

Lectures and weekly exercises.

Assessment methods

60% Written exam, 40% assessed homework tasks.

Resources

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum information theory
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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