402-0462-00L  Advanced Topics in Quantum Information Theory

SemesterSpring Semester 2022
LecturersL. Pacheco Cañamero B. del Rio, R. Silva
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
402-0462-00 VAdvanced Topics in Quantum Information Theory3 hrs
Wed09:45-11:30HIL E 8 »
Thu12:45-13:30HPT C 103 »
L. Pacheco Cañamero B. del Rio, R. Silva
402-0462-00 UAdvanced Topics in Quantum Information Theory1 hrs
Wed11:45-13:30HIL E 8 »
L. Pacheco Cañamero B. del Rio, R. Silva

Catalogue data

AbstractSolid introduction on advanced topics in quantum information theory, including: quantum thermodynamics, quantum clocks and control, measurement theory, quantum learning theory and quantum foundations.

Pre-requisites: Quantum Information Theory or equivalent courses.
Learning objectiveTo prepare master students for a PhD or industry career by providing a selection of active research topics in quantum information theory and related areas.
Content1. Quantum thermodynamics

a) Virtual qubits, virtual temperatures
b) Qubit swaps
c) Passivity and complete passivity
d) Equilibration, Jaynes principle, thermal states and baths
e) Resource theories: noisy operations, majorization and entropy
f) Resource theories: thermal operations, thermal majorization and free energy
g) Maxwell’s demon and Szilard’s engine, Landauer erasure
h) Thermodynamics protocols for finite-size systems
i) Autonomous thermal machines: master equation, continuous dynamics, steady states
j) Autonomous thermal machines: types of engines, working regimes

2. Clocks and control

a) Ideal quantum clocks
b) Quasi-ideal clocks
c) Information-theoretical analysis


3. Puzzles and no-go theorems

a) Hardy’s experiment (setup, simplified version, logical analysis)
b) Quantum pigeonhole experiment (setup, simplified version, logical analysis)
c) Physical implementation of measurements (von Neumann measurement scheme, strong and weak measurements, weak values)
d) Replacing counterfactuals with weak measurements (Hardy and pigeonhole experiments)
e) Replacing counterfactuals with measurements by different agents (Frauchiger-Renner experiment)
f) Pre- and post-selection paradoxes: definition and example
g) Contextuality: operational definition and relation to paradoxes


4. Quantum learning theory (guest lecturer Marco Tomamichel)

Quantum learning theory provides the theoretical foundations for machine learning involving quantum objects, where the quantum aspect can either come from the learner itself (e.g. quantum algorithms for machine learning) or the object to be studied (e.g. state tomography), or both. Quantum information theory tools can establish fundamental limits for such learning tasks. We will in particular explore applications of information theory to the following learning tasks:

a) Sample-optimal learning of quantum states
b) Quantum PAC learning
c) Multi-armed quantum bandits
Lecture notesProvided for the majority of contents; hand-written lecturer notes for the rest.
LiteratureSelected papers will be recommended to read throughout the semester. For example, for the quantum learning part:

[1] Haah et al., Sample-optimal tomography of quantum states, arXiv:1508.01797.

[2] Arunachalam and de Wolf, Optimal Quantum Sample Complexity of Learning Algorithms, arXiv:1607.00932.

[3] Lumbreras et al., Multi-armed quantum bandits: Exploration versus exploitation when learning properties of quantum states, arXiv:2108.13050.
Prerequisites / NoticeQuantum Information Theory or equivalent course is necessary. Students should be familiar with density matrices, quantum channels (TPCPMs), Hamiltonian evolution and partial trace. Familiarity with quantum entropy measures helps but is not strictly necessary.
CompetenciesCompetencies
Subject-specific CompetenciesConcepts and Theoriesassessed
Techniques and Technologiesassessed
Method-specific CompetenciesAnalytical Competenciesassessed
Decision-makingfostered
Media and Digital Technologiesfostered
Problem-solvingassessed
Project Managementfostered
Social CompetenciesCommunicationassessed
Cooperation and Teamworkfostered
Customer Orientationfostered
Leadership and Responsibilityfostered
Self-presentation and Social Influence fostered
Sensitivity to Diversityfostered
Negotiationfostered
Personal CompetenciesAdaptability and Flexibilityfostered
Creative Thinkingassessed
Critical Thinkingassessed
Integrity and Work Ethicsfostered
Self-awareness and Self-reflection fostered
Self-direction and Self-management fostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits8 credits
ExaminersL. Pacheco Cañamero B. del Rio, R. Silva
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 120 minutes
Written aidsNone
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Only public learning materials are listed.

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Offered in

ProgrammeSectionType
Physics MasterSelection: Theoretical PhysicsWInformation
Quantum Engineering MasterElectivesWInformation