Methods in Quantum Technologies: theory and applications

Period of duration of course
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Course info
Number of course hours
40
Number of hours of lecturers of reference
40
Number of hours of supplementary teaching
0
CFU 6
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Modalità esame

Oral exam

Programma

Open quantum systems

(a) Brief recap of the basic properties.  Kraus and Stinespring representations

(b) CPT theorem

(c) Choi-Jamiolkowski isomorphism 

(d) Composition rules

(e) Adjoint channel

(f) Spectral properties

(g) Vectorial representation 

(h) Examples 

(i) Qubit channels 

(j) Complementary channels: anti-deg and degrability

(k) Quantum Operations

(l) Bosonic Quantum channels 

2. Dynamical Semigroups: Master Equation (ME) and Lindblad form

(a) Time evolution in continous time. Divisibility. 

(b) General properties

(c) Gauge invariance invariance of Lindblad operators. 

(d) Formal derivation of the ME

(e) Microscopical deriviation of the ME

(f) Examples 

(g) Collisional models 

3. Classical informaton theory 

(a) Shannon entropy

(b) Shannon theorem I

(c) Joint entropy and conditional entropy

(d) Mutua information; data processing, subaddivity and Fano inequality

(e) Shannon theorem II 

(f) Transmission rate and capacities

4. Entropy in quantum mechanics 

(a) Von Neuman entropy 

(b) Subadditivity, s-subadditivity etc

(c) Connection with thermodynamics

(d) Schumacher compression.

(e) Accessible information

(f) Holevo Bound

5. Quantum Communication

(a) CPT maps and their capacities.

(b) Classical capacitiy (HSW theorem) 

(c) Quantum capacity and coherent information

(d) Entanglement assisted capacities 

5. Quantum Metrology 

(a) Quantum Cramer-Rao bound: Heisenberg vs SQL

(b) Chernoff inequality 

6. Many body systems 

(a) MPS decomposition

Obiettivi formativi

Advanced course on QINFO

Riferimenti bibliografici

A. S. Holevo, Quantum Systems, Channels, Information A Mathematical Introduction (De Gruyter Studies in Mathematical Physics