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Courses

Marcelo Martinelli (Universidad de São Paulo, Brazil): Multipartite entanglement and sudden death in Quantum Optics:  continuos variables domain.

Parametric Amplifiers and Oscillators are usual sources of non-classical states of light, either in the domain of photon counting (discrete variable) or in the domain of continuous variables.

We will present their application for the generation of entangled light beams, either with degenerate wavelengths or with different colors. Moreover, we will discuss the control of the noise sources that can ruin this entanglement.

These spurious noise sources can affect the output fields, resulting in the production of fragile entangled states (states that can disentangle during the interaction with the environment) that are reminiscent of the Entanglement Sudden Death occurring in the discrete variables domain. We will also discuss the benchmarks that should be obtained to produce robust entanglement among these fields.

  • Entangled states in the continuous variable domain.
  • Measurement of quadratures of the EM field: homodyne and self-homodyne techniques.
  • Manipulation of the field state: squeezed state and entangled states generation by second order nonlinearities.
  • Applications of entangled states in quantum information processing.
  • Environment effects on the entanglement: fragile and robust entangled states.

Bibliography

  • Walls, “Quantum Optics”.
  • A. Peres,  Phys. Rev. Lett. 77, 1413–1415 (1996).
  • Lu-Ming Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722–2725 (2000).
  • R. Simon,  Phys. Rev. Lett. 84, 2726–2729 (2000).

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Paolo Mataloni (Universidad di Roma, Italia): Generation and application of n-qubit hyperentangled photon states.

Multiqubit photon states are a basic instrument for many quantum information tasks, dealing both with foundational concepts and with advanced communication and computation protocols. As an example, the nonlocal behaviour of a quantum state and the computational power of a quantum computer grow with the number of qubits. In quantum optics entangled states of two photons are realized by using parametric down conversion and different approaches. Qubits may be encoded in a particular degree of freedom (DOF) of the particles, such as polarization, momentum (regarding linear, orbital, and transverse spatial modes), energy-time and time bin.

In order to improve the wide possibilities offered by quantum mechanics, more qubits must be encoded in a quantum state. Two approaches may be followed on this purpose. The first one consists of increasing the number of entangled particles. Multiqubit states are created by
distributing the qubits between the particles in such a way that each particle carries one qubit. A second strategy is to encode more than one qubit in each particle, by exploiting different DOFs of the photons. Entangling two particles in different DOFs corresponds exactly to generate a
hyperentangled state.

In this course I will present and discuss the basic principles of the concept of hyperentanglement, with particular emphasis to the following topics:

  • Experimental realization of hyperentangled photon states.
  • Characterization and measurement of hyperentangled states.
  • Hyperentanglement and quantum nonlocality.
  • Hyperentanglement for quantum information and quantum computation protocols.

Some references on hyperentanglement can be found in the Rome quantum optics group’s webpage: http://quantumoptics.phys.uniroma1.it

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Wallon Nogueira (Center for Optics and Photonics (CEFOP), UDEC, Chile): Two-photon interferometry and Complementarity

We will present the results of a research performed in the laboratories of quantum optics at Universidad de Concepción about Complementarity relations and two-photon interference for Hybrid Photonic States, which is a topic of investigation that has received an increasing amount of attention. The presentation will be separated in the subtopics:

  • Brief review of Spontaneous Parametric Down-conversion;
  • Two-photon interferometry and Complementarity;
  • Hybrid photonic entanglement;
  • One- and two-photon probability distributions;
  • Preparing a Hybrid Photonic State;
  • Experimental results and discussion.

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Luis Orozco (Univeristy of Maryland, USA): Introduction to Quantum Optics for Cavity QED

These five lectures will present an introduction to Quantum Optics using Cavity QED as the background system.

  • Correlations in optics, the semiclassical method in quantum optics.
  • Quantum correlations of the intensity and the field.
  • Conditional dynamics in quantum systems.
  • Towards quantum feedback.
  • Hybrid systems.

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Sebastião de Pádua (Universidade Federal de Minas Gerais, Brazil): Spatial correlations in parametric down-conversion.

The transverse spatial effects observed in photon pairs produced by parametric down-conversion provide a robust and fertile testing ground for studies of quantum mechanics, non-classical states of light, correlated imaging and quantum information. This mini course will be given in four lectures:

  • Fundamentals of parametric down-conversion
  • Fundamentals of spatial correlations
  • Double slit experiments with twin photons and quantum imaging
  • Applications to quantum information

Bibliography:

  • S. P. Walborn, C.H. Monken, S. Pádua, and P.H. Souto Ribeiro, “Spatial correlations in parametric down-conversion”, Physics Reports 495, pp. (2010)

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Aephraim Steinberg (University of Toronto, Canada): Photons, quantum measurement and quantum information.

Partial, approximate, table of contents:

Lecture 1:

Quantum States of Light and Quantum Interference

  • Single photons and classical beams
  • Optical coherence and quantum uncertainty
  • Two-photon interference, quantum erasers, etc.
  • Bell’s inequalities

Lecture 2:

A modern perspective on quantum measurement

  • Projective measurements and POVMs
  • Density matrices and reduced density matrices
  • von Neumann measurements and back-action
  • Entanglement and decoherence
  • Weak measurement
  • Interaction-free measurement and Hardy’s Paradox
  • Resolving the Bohr-Einstein debates
  • Measuring Bohm trajectories

Lecture 3:

Quantum optical experiments on measurement & information

  • No-cloning theorem
  • Quantum cryptography
  • Quantum teleportation
  • Tomography & avoiding it
  • Post-selective nonlinearity, linear quantum-optical quantum computing
  • Entangled states for precision measurement

Bibliography:

  • Nielsen & Chuang, Quantum Computation and Quantum Information (Cambr. Univ. Press, 2000).
  • Gerry & Knight: Introductory Quantum Optics (Cambr. Univ. Press 2004).
  • Feynman’s QED: the strange theory of light and matter.
  • Bell’s Speakable and unspeakable in Quantum Mechanics.
  • An Introduction to Quantum Measurement Theory by Kurt Jacobs, in preparation at Cambridge University Press; several chapters are available at http://www.quantum.umb.edu/Jacobs/books.html.
  • QO review: Steinberg, Chiao, Kwiat, in AIP AMO Physics Handbook, edited by G.W.F. Drake (http://www.physics.utoronto.ca/~steinber/Quantum_Optical.pdf).
  • QO for QI review: Pan, Chen, Zukowski, Weinfurter, Zeilinger, arXiv:0805.285 (and many references therein).

More links available at http://www.physics.utoronto.ca/~aephraim/aephraim.html as well.

For a fuller treatment of the more rigorous and mathematical material, common references include  von Neumann’s Mathematical Foundations of Quantum Mechanics Braginsky, Khalili, and Thorne’s Quantum Measurement Helstrom’s Quantum Detection and Estimation Theory.

Some light introductions to some of the topics we will discuss include Zurek, “Decoherence and the transition from quantum to classical,” Physics Today 44, 36 (1991) and Horgan, “Quantum Philosophy,” Sci. Am. 267 (1), 94 (7/92).

Some references to my own group’s recent work in quantum measurement can be found at http://www.physics.utoronto.ca/~aephraim/QMsmt.html.

A wordy description of weak measurement, along with a long list of references, may be found in Speakable and Unspeakable, Past and Future, A.M. Steinberg, in SCIENCE AND ULTIMATE REALITY: Quantum Theory, Cosmology and Complexity, edited by Barrow, Davies, and Harper.