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B021037 - QUANTUM INFORMATION
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Sustainable Development Goals 2030
Academic Year 2023-24
Course year
First year - Second Semester
Belonging Department
Physics and Astronomy
Course Type
Single education field course
Scientific Area
FIS/03 - PHYSICS OF MATTER
Credits
6
Teaching Hours
48
Teaching Term
19/02/2024 ⇒ 14/06/2024
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Mutuality
Course teached as:
B021037 - INFORMAZIONE QUANTISTICA
Second Cycle Degree in PHYSICAL AND ASTROPHYSICAL SCIENCES
Curriculum FISICA DELLA MATERIA
B021037 - INFORMAZIONE QUANTISTICA
Second Cycle Degree in PHYSICAL AND ASTROPHYSICAL SCIENCES
Curriculum FISICA DELLA MATERIA
Teaching Language
Italian (English if required)
Course Content
Title:
QUANTUM INFORMATION
Elements of quantum information theory: from entanglement to open quantum systems dynamics, via the quantum measurement process.
Theory of open quantum systems, i.e. interacting with the external environment: from quantum maps to the analysis of entropy and information, from error correction to optimal control theory, towards the new millennium quantum technologies.
QUANTUM INFORMATION
Elements of quantum information theory: from entanglement to open quantum systems dynamics, via the quantum measurement process.
Theory of open quantum systems, i.e. interacting with the external environment: from quantum maps to the analysis of entropy and information, from error correction to optimal control theory, towards the new millennium quantum technologies.
Suggested readings (Search our library's catalogue)
- M.A. Nielsen and I.A. Chuang, "Quantum computation and quantum information", Cambridge University Press (2003).
- M.W. Wilde, "Quantum Information Theory", Cambridge University Press (2013).
- H.-P. Breuer and F. Petruccione, "The theory of open quantum systems", Oxford University Press (2002).
- I. Bengtsson and K. Zyczkowski, "Geometry of quantum states", Cambridge University Press (2006).
- P. Kaye, R. Laflamme, M. Mosca, "An introduction to Quantum Computing", Oxford University Press (2007).
- T. Heinosaari and M. Ziman, "The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement", Cambridge University Press (2011).
- M.W. Wilde, "Quantum Information Theory", Cambridge University Press (2013).
- H.-P. Breuer and F. Petruccione, "The theory of open quantum systems", Oxford University Press (2002).
- I. Bengtsson and K. Zyczkowski, "Geometry of quantum states", Cambridge University Press (2006).
- P. Kaye, R. Laflamme, M. Mosca, "An introduction to Quantum Computing", Oxford University Press (2007).
- T. Heinosaari and M. Ziman, "The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement", Cambridge University Press (2011).
Learning Objectives
Aim of this course is to help the students acquiring
- knowledge of the formal and conceptual tools of quantum information theory, with attention focused upon those needed in the analysis of recent advances in quantum communication, quantum computation, and quantum technologies in general;
- understanding the difference between classical and quantum information theory, particularly as far as the different measurement process is concerned;
- skills for effectively exploit the relation between quantum information theory and open quantum systems dynamics in the framework of quantum technoloties.
- knowledge of the formal and conceptual tools of quantum information theory, with attention focused upon those needed in the analysis of recent advances in quantum communication, quantum computation, and quantum technologies in general;
- understanding the difference between classical and quantum information theory, particularly as far as the different measurement process is concerned;
- skills for effectively exploit the relation between quantum information theory and open quantum systems dynamics in the framework of quantum technoloties.
Prerequisites
Quantum Mechanics and related mathematical tools, with special relevance of those pertaining advanced linear algebra.
Teaching Methods
Lectures at the blackboard, with examples and exercises. Some lectures will be complemented with images and video projections.
Further information
Office hours: on appointment
Emails:
filippo.caruso@unifi.it
leonardo.banchi@unifi.it
Websites:
https://www.qdab.org
https://paolaverrucchi.weebly.com
Emails:
filippo.caruso@unifi.it
leonardo.banchi@unifi.it
Websites:
https://www.qdab.org
https://paolaverrucchi.weebly.com
Type of Assessment
The exam consists of a colloquium at the blackboard of about 3/4 of an hour. Three options are available to the student: 1) traditional oral exam on the course programme, 2) seminar on a scientific publication previously discussed with the professor, 3) lesson on a topic being randomly chosen from the list below.
1 - Foundations of Classical Information Theory: from the bit definition to the first Shannon theorem (including typical sequences theorem).
2 - Second Shannon Theorem and connections among information, entropy and channel capacity.
3 - First postulate of QM and unitary dynamical evolution: qubit, Bloch sphere and single-qubit logical gates.
4 - Measurement postulate: POVM and PVM; indistinguishability of non-orthogonal states.
5 - Composite systems, partial trace and density operator as subsystem state: Schmidt decomposition and Entanglement.
6 - Measurement-like dynamics, decoherence and Ozawa model.
7 - Entanglement for mixed states: von Neumann entropy, one-tangle and concurrence.
8 - Quantum state and process tomography.
9 - Indistinguishability of non-orthogonal states, no-cloning theorem, superdense coding and quantum teleportation.
10 - Open quantum system dynamics: universal dynamical maps.
11 - Bell inequalities.
12 - Representations of quantum CPTP maps.
13 - Examples and properties of quantum channels.
14 - One-qubit quantum channels.
15 - Distance measures between quantum states.
16 - Entropy: from Shannon to von Neumann.
17 - Quantum version of the first Shannon theorem.
18 - Quantum version of the second Shannon theorem.
19 - Capacities of quantum channels.
20 - Quantum cryptography.
21 - Deutsch-Josza and quantum parallelism.
22 - Quantum circuits and examples.
23 - Grover algorithm.
1 - Foundations of Classical Information Theory: from the bit definition to the first Shannon theorem (including typical sequences theorem).
2 - Second Shannon Theorem and connections among information, entropy and channel capacity.
3 - First postulate of QM and unitary dynamical evolution: qubit, Bloch sphere and single-qubit logical gates.
4 - Measurement postulate: POVM and PVM; indistinguishability of non-orthogonal states.
5 - Composite systems, partial trace and density operator as subsystem state: Schmidt decomposition and Entanglement.
6 - Measurement-like dynamics, decoherence and Ozawa model.
7 - Entanglement for mixed states: von Neumann entropy, one-tangle and concurrence.
8 - Quantum state and process tomography.
9 - Indistinguishability of non-orthogonal states, no-cloning theorem, superdense coding and quantum teleportation.
10 - Open quantum system dynamics: universal dynamical maps.
11 - Bell inequalities.
12 - Representations of quantum CPTP maps.
13 - Examples and properties of quantum channels.
14 - One-qubit quantum channels.
15 - Distance measures between quantum states.
16 - Entropy: from Shannon to von Neumann.
17 - Quantum version of the first Shannon theorem.
18 - Quantum version of the second Shannon theorem.
19 - Capacities of quantum channels.
20 - Quantum cryptography.
21 - Deutsch-Josza and quantum parallelism.
22 - Quantum circuits and examples.
23 - Grover algorithm.
Course program
Axioms of Quantum Mechanics and elements of quantum computation: states and qubits, Majorana-Bloch sphere, evolution and logical gates, states of composite systems and entanglement, Bell states. Quantum measurement process according to the minimal interpretation (projective measurement and POVM). The Bell inequality.
Tools for information theory:
Information content and entropy, Shannon theorems. Von Neumann entropy and entanglement of formation. Entanglement measures and estimators. Distance between quantum states.
Open quantum systems dynamics:
Decoherence and dissipation. Universal dynamical maps. Quantum maps, system-environment interaction and Kraus operators. Single-qubit quantum maps and examples. Quantum state and process tomography. Measures of quantum information and properties. Quantum versions of Shannon theorems. Capacities of quantum channels. Quantum cryptography and error correction. Quantum parallelism and Deutsch-Josza. Quantum Fourier Transform and applications, as Shor and Grover algorithms. Physical implementations: from quantum biology to the controlled manipulation of atomic, molecular and photonic systems, and even the more recent quantum machine learning.
Tools for information theory:
Information content and entropy, Shannon theorems. Von Neumann entropy and entanglement of formation. Entanglement measures and estimators. Distance between quantum states.
Open quantum systems dynamics:
Decoherence and dissipation. Universal dynamical maps. Quantum maps, system-environment interaction and Kraus operators. Single-qubit quantum maps and examples. Quantum state and process tomography. Measures of quantum information and properties. Quantum versions of Shannon theorems. Capacities of quantum channels. Quantum cryptography and error correction. Quantum parallelism and Deutsch-Josza. Quantum Fourier Transform and applications, as Shor and Grover algorithms. Physical implementations: from quantum biology to the controlled manipulation of atomic, molecular and photonic systems, and even the more recent quantum machine learning.