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Lecture

Quantum Measurement: General Description

In course

PHYS-758: Advanced Course on Quantum Communication

The aim of this doctoral course by Nicolas Sangouard is to lay the theoretical groundwork that is needed for students to understand how to take advantage of quantum effects for communication technologies and contribute to on-going efforts in this field. ...

Description

This lecture covers the general description of quantum measurements, including the post-measurement state, Kraus operators, and auxiliary systems. The instructor explains the concept of satisfying rules and provides examples of measurement results.

Instructor

Christophe Marcel Georges Galland

I studied at Ecole Polytechnique in Paris (X2003) and received my PhD in 2010 from ETH Zürich for a thesis in solid-state quantum optics with individual carbon nanotubes, in the Quantum Photonics Group of Prof. Ataç Imamoglu. As a postdoctoral researcher at Los Alamos National Lab (USA) I studied the photophysics of individual nanocrystal quantum dots in the groups of Victor Klimov and Han Htoon. I was investigating the mechanisms responsible for fluorescence fluctuations and how to control them. I then moved to the University of Delaware in the group of Michael Hochberg to work in the emerging field of integrated quantum optics. I was leading international projects such as the realisation of an on-chip source of quantum correlated photons integrating optical filters and demultiplexers. From 2013 to 2016, I was working at EPFL in the group of Prof. Kippenberg in the field of quantum optomechanics with an Ambizione Fellowship of the Swiss National Science Foundation (SNSF). My work focused on the creation of non-classical vibrational states of mesoscopic oscillators and on the amplification of vibrations in molecules. Since May 2017, I am leading the Laboratory of Quantum and Nano-Optics at EPFL as an SNSF-funded professor in the Institute of Physics. My team investigates two main phenomena: (i) the vibrational dynamics of molecules embedded in nanoscale plasmonic cavities, and (ii) non-classical correlations mediated by individual quanta of crystal vibrations at room-temperature. We employ state-of-the-art spectroscopic tools such as femtosecond lasers and single-photon counters to get new insights into sub-nanometer scale dynamics.

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

Related concepts (32)

Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

Choi's theorem on completely positive maps

In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. An infinite-dimensional algebraic generalization of Choi's theorem is known as Belavkin's "Radon–Nikodym" theorem for completely positive maps. Choi's theorem. Let be a linear map. The following are equivalent: (i) Φ is n-positive (i.e. is positive whenever is positive). (ii) The matrix with operator entries is positive, where is the matrix with 1 in the ij-th entry and 0s elsewhere.

Quantum channel

In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet. More formally, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum operation viewed not merely as the reduced dynamics of a system but as a pipeline intended to carry quantum information.

Quantum Zeno effect

The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be slowed down by measuring it frequently enough with respect to some chosen measurement setting. Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state.

Weak measurement

In quantum mechanics (and computation & information), weak measurements are a type of quantum measurement that results in an observer obtaining very little information about the system on average, but also disturbs the state very little. From Busch's theorem the system is necessarily disturbed by the measurement. In the literature weak measurements are also known as unsharp, fuzzy, dull, noisy, approximate, and gentle measurements. Additionally weak measurements are often confused with the distinct but related concept of the weak value.

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