**Course Number: ECE 623, PHYSICS 623**

Fall 2023

This course is mainly focused on Quantum Information theory, and more specifically, Quantum Shannon theory. In the light of quantum mechanics, classical concepts such as information, bit, entropy, mutual information, data compression, and channel capacity, should be modified to take into account quantum effects. Similar to its classical version, the primary motivation for quantum information theory is the theory of communication. Interestingly, it turns out that by taking advantage of quantum phenomena, such as information-disturbance principle, distant parties can communicate with a level of privacy, which is unattainable classically.

Applications of this field are not limited to the communication theory. Quantum information theory has found applications in different areas of physics, from topological order, and many-body systems to quantum thermodynamics, quantum gravity and black holes. Also, the ideas and tools developed in this theory are crucial for understanding quantum noise and decoherence. Furthermore, this theory provides a framework for understanding and quantifying entanglement and other quantum resources such as coherence.

**Day/Time:** Monday-Wednesday 4:40PM to 5:55PM

**Instructor: **Iman Marvian

**Textbooks****:**

**Quantum Information Theory (**Mark Wilde)- Quantum Computation and Quantum Information (Michael Nielsen, Isaac Chuang)

Both textbooks are available online at Duke library website.

**Tentative Syllabus:**

- Quick Review of Density Matrix formalism
- Noisy quantum dynamics, Quantum Channels, Choi operator, Kraus decomposition, Qubit Channels
- Distinguishability measures (Trace distance and its operational interpretation, Diamond norm, Uhlman Fidelity)
- Classical Information and Entropy (entropy, conditional entropy, mutual information, relative entropy, data processing inequality)
- Quantum Information and Entropy (von Neumann entropy, coherent information, quantum mutual information, Holevo information, conditional entropy, mutual information, Quantum relative entropy, strong subadditivity, data processing inequality)
- Classical and Quantum typicality, Schumacher compression
- Classical and Quantum Capacities of Quantum channels (HSW and LSD theorems)
- Entanglement Manipulation (Local Operations and Classical Communication, Nielsen’s theorem), Entanglement dilutions and Concentrations, Quantum Resource theories

Assignments will be posted on Sakai.