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2018　Quantum Information

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Academic unit or major
Graduate major in Physics
Instructor(s)
Hosoya Akio 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H115)  Fri3-4(H115)  
Group
-
Course number
PHY.Q435
Credits
2
Academic year
2018
Offered quarter
4Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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.

Keywords

EPR paradox, violation of Bell’s inequality, degree of entanglement, mutual information,POVM
Maxwell’s demon,Holevo bound and uncertainty principle.

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills ✔ Critical thinking skills Practical and/or problem-solving skills

Class flow

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

  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

Textbook(s)

none

Reference books, course materials, etc.

M. A. Nielsen and I. L. Chuang, "Quantum Computation and Quantum Information"
(Cambridge University Press, Cambridge, 2000).

Assessment criteria and methods

Scored by a term report

Related courses

  • ZUB.Q204 ： Quantum Mechanics I
  • MCS.T204 ： Introduction to Computer Science
  • ZUQ.T211 ： Basic Theory of Information Processing

Prerequisites (i.e., required knowledge, skills, courses, etc.)

none

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