After reviewing the principles of quantum mechanics and classical information theory, the lecture on the basics of the world standard quantum information science will be given.
Understanding the basic concepts like POVM in the generalized measurement theory, students are encouraged to master the standard
tools like the Kraus operators. Ultimate target is the Holevo bound and uncertainty principle.
EPR paradox, violation of Bell’s inequality, degree of entanglement, mutual information,POVM
Maxwell’s demon,Holevo bound and uncertainty principle.
✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | Practical and/or problem-solving skills |
After recapitulating the previous lecture, the main lectures will resume.
Students are asked to do a homework to consolidate the understanding.
Course schedule | Required learning | |
---|---|---|
Class 1 | Axioms of quantum mechanics(1) | Understand the superposition principle, and the Schrodinger equation |
Class 2 | Axioms of quantum mechanics(2) | Understand the Born rule, the tensor product density operator |
Class 3 | density operator | Understand the mixed state |
Class 4 | spin | Understand the Bloch sphere, Control by a magnetic field, the Stern-Gerlach experiment |
Class 5 | EPR paradox | Understand the non-locality, the physical reality |
Class 6 | entanglement | Understand the violation of Bell's inequality |
Class 7 | classical information theory | Understand the Shannon entropy, the data compression |
Class 8 | relative entropy | Understand the mutual inforamation |
Class 9 | Maxwell’s demon | Understand the information and thermodynamics |
Class 10 | Von Neumann entropy | Understand the various inequalities among quantum information entropies |
Class 11 | Generalized measurement theory | Understand the POVM, the Kraus representation |
Class 12 | Holevo bound | Understand the maximum information |
Class 13 | Completely positive map | Understand the measurement model |
Class 14 | Uncertainty principle | Understand the Ozawa’s inequality |
Class 15 | Weak value/weak measurement | Consider the probabilistic interpretation |
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M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information"
(Cambridge University Press, Cambridge, 2000).
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