Course

Unit 1

Introduction: quantum states, density matrix formalism, measurement operators, positive operator valued measures.

Unit 2

Quantum channels, Examples of Quantum channels, Multipartite quantum systems, Entanglement.

Unit3

Quantum data compression: Shannon entropy, classical lossless source coding theorem, von Neumann entropy and its properties, Quantum data compression.

Unit 4

Schumacher’s noiseless quantum coding theorem, accessible information and Holevo bound, classical noisy channel coding theorem, quantum mutual information.

Unit 5

Entanglement assisted communication, entanglement assisted capacity theorem, quantum capacity theorem, examples of capacity of quantum channels.

Evaluation Pattern

Course Description

This course builds on prior quantum computing knowledge, introducing the information-theoretic foundations of quantum systems. Students will study quantum states, channels, entropy, and communication protocols, with a focus on theoretical concepts and essential calculations.

Course Outcomes

On successful completion of the course, students shall be able to

1. Apply the density matrix formalism and measurement operators to analyse quantum states and perform basic calculations related to positive operator-valued measures (POVMs).
2. Identify and explain different types of quantum channels and apply theoretical concepts to analyse the transmission of quantum information in multipartite quantum systems, with a focus on entanglement properties.
3. Apply Shannon entropy and von Neumann entropy to solve problems in quantum data compression, demonstrating an understanding of classical and quantum information theory principles.
4. Understand and apply Schumacher’s noiseless quantum coding theorem, the Holevo bound, and quantum mutual information, with supporting calculations related to classical noisy channels and quantum information transfer.
5. Explain and analyse the principles of entanglement-assisted communication and quantum capacity theorems, applying these concepts to calculate the capacity of simple quantum channels.

Textbooks

1. M.M. Wilde, Quantum Information Theory, 2nd Edition, Cambridge University Press (2017)
2. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, 10th Anniversary Ed., Cambridge University Press (2010)

References

1. Cover T M and Thomas J A, Elements of Information Theory, 2nd Edition, Wiley (2013).
2. Parthasarathy K R, Coding Theorems of Classical and Quantum Information Theory, 2nd Edition, Hindustan Book Agency (2013)
3. Michael Sipser, Introduction to the Theory of Computation, 3^rd Ed, Cengage Learning India (2014)
4. C. Macchiavello, G. M. Palma, A. Zeilinger, Quantum Computation and Quantum Information Theory, World Scientific (2001). Contains selected foundational research articles and references to many more.