Stony Brook Physics

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Entanglement in quantum
Stony Brook
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  • Prof. Vladimir Korepin
    C.N. Yang Institute for Theoretical Physics
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Quantum Information and Physics

Spring 2022, Physics 680-01, Class Number 46401
Physics building room P123.
Tuesday and Thursday from 8:00am till 9:20am.
Physics building P123. In person.
Office Hours: Tuesday and Thursday from 9:30 am till 10am.
Mid-term exam on March 10.
Final Exam on May 5.

Course description

The course will start with a brief reminder of quantum mechanics. All sections of quantum mechnics necessary for information processing will be introduced: interaction with the environment, measurements theory, trace preserving completely positive maps [super-operators], as well as Bell's inequalities. Master equation and Lindblad operators are important for description of open quantum systems. The course will proceed to entanglement theory. Application of entanglement of dynamical systems [including high energy]: scaling of von Neumann and Renyi entropy with the size of the box. Dynamics of entanglement entropy including quenches and Cardy-Calabrese formula. Holographic approach to entanglement and structure of entanglement in quantum field theory.
Information theory [starting from Shannon's theorems, describibng channel capacity] will be related to statistical physics [including Maxwell's demon and Landauer's Principle] and probability theory. Holevo's information helps to describe noisy quantum channels. Quantum teleportation and cryptography will be explained. Information loss in black holes will be discussed.
Algorithm theory: Shor's and Grover's quantum algorithms [also quantum counting and phase estimation]. Measures of complexity of quantum algorithms will be illustrated. We shall have a lecture on qiskit. Variational quantum algorithms will be included. Also an input of Bethe Ansatz wave-function in a quantum computer. Error resistant version of quantum search also will be mentioned. Different approaches to building of quantum computers: solid state [Josephson junction], topological, chiral and quantum optics. Different architectures of quantum computation: circuit, adiabatic, topological and measurement based quantum computation. Quantum cellular automata will be explained.
Application of ideas of quantum information to condensed matter, nuclear physics and elementary particles also will be explained: the entropy of jets, deep inelastic scattering, Lipatov's spin chain, Schwinger model, Thirring model and sine-Gordon, Zamolodchikov C-theorem, XXZ spin chain, AKLT spin systems, Lieb-Linger model of anyons, Kitaev model, Kondo model, Hubbard model and SYK model. Simulation of models of mathematical physics in optical lattices also will be explained.
Computational physics also will be mentioned: matrix product states and relation to algebraic Bethe ansatz. Highly entangled spin chains [Motzkin and Fredkin] will be mentioned. The entanglement entropy becomes extensive in these models [proportional to the volume] after q-deformation.
Quantum machine learning will be explained, including classical machine learning. Integrable spin chains and cellular automata [such as Rule 54] will be included. Also quantum technique in stochastic mechanics will be touched upon.
Guest lecturers will be invited. Quantum information learning club will be organized.

Requirements: Knowledge of linear algebra is required. Students should know physics and quantum mechanics on the undergraduate level.

Learning outcomes

  • Application of information theory to physics. Entanglement in high energy physics
  • Understanding of information theory and its relation to statistical mechanics and probability theory
  • Quantum mechanics of open systems and interaction with environment
  • Quantum machine learning.

90% of final grade is based in exam and 10% on homework         

For your information. If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at They will determine with you what accommodations are necessary and appropriate. All information and documentation are confidential.
Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site
Disability Support Services, Academic Integrity and Critical Incident Management, see

Email: vladimir dot korepin at