Ohiko deialdia: orientazioak eta uko egitea

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Irakasgai-zerrenda

- Introduction: What is quantum information? Subfields of quantum information science.



- General characteristics of multi-partite quantum systems: Classical, Quantum and Multi-qubit systems (pure states); Measurement; Mixed states and the density matrix; Fidelity; Geometry of quantum states; Qubits; Qudits (Qunits): d-dimensional systems; Higher dimensional systems.



- Interesting quantum states: Bipartite singlet state; Werner states; Schrödinger cat states; Greenberger-Horne-Zeilinger (GHZ) state.



- Bell inequalities: EPR paradox; Local hidden variable models; The CHSH Bell inequality; Loopholes; Detection efficiency loophole; Locality loophole; Mermin’s inequality.



- Entanglement theory: Bipartite case; Pure states; Mixed states; Entanglement criteria; Partial transposition; Entanglement witnesses; Variance based criteria; Multipartite case.



- Entanglement measures: Positive Operator Valued Measure; Local operations and classical communication; Von Neumann entropy; Entanglement of formation and of distillation; Bound entanglement; Requirements for entanglement measures.



- No-go theorems and related issues: No-cloning Theorem; Measurement problem; Quantum teleportation; Imperfect cloning; Quantum cryptography; One-time Pad; Quantum money (70’s); BB84; Ekert protocol (E91); Quantum metrology.





- Introduction to Quantum Computation: Why quantum computation? Some quantum algorithms are much faster than their classical counterparts.



- Quantum Circuit Model: A standard model for universal quantum computation. Quantum bits, qubits. Inputs, logical gates, outputs. Equivalent universal quantum computation models such as One-way quantum computation, Adiabatic quantum computation, etc.



- DiVincenzo’s criteria: Well-defined qubits. Initialization to a pure state. Universal set of quantum gates. Measurement. Long coherent time.



- Universal quantum computation: proof of universality: one-qubit gates plus CNOT.



- Physical realizations of universal quantum computation: universal gate sets in physical

settings such as NMR, trapped Ions, linear optics, quantum dots, superconducting etc.



- Quantum Error Correction: Introduction to passive and active Error correction protocols: decoherence free subspace, dynamical decoupling (or Spin-echo, Bang-Bang control etc.) and universal quantum error correction codes.



- Quantum Algorithms: Shor’s Algorithm, Grover’s algorithm and quantum simulation.

Bibliografia

Oinarrizko bibliografia

I. Bengtsson and K. Zyczkowski, Geometry of Quantum States, An Introduction to Quantum Entanglement, Cambridge University Press, 2009.

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2011).

O. Gühne and G. Tóth, Entanglement detection, Phys. Rep. 474, 1 (2009).

G. Tóth and I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A: Math. Theor. 47, 424006 (2014), special issue "50 years of Bell's theorem”.

Gehiago sakontzeko bibliografia

R, P, M and K Horodecki, Quantum entanglement, Rev Mod Phys 81, 865 (2009)



O Guhne and G Tóth, Entanglement detection, Phys Rep 1-75 (2009)