Lecture

Quantum Measurement: Wave Function Collapse and Operators

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In course

MICRO-444: La science quantique : une vision singulière

Les étudiants comprennent les caractéristiques de la science quantique. Ils en maitrisent le formalisme et l'appliquent dans les systèmes de base: puits, fils et boites quantiques, qubits. ...

Description

This lecture discusses the principles of quantum measurement, focusing on the concept of wave function collapse during singular measurements. The instructor explains how the wave function collapses onto an eigenstate of the measurement apparatus, using examples such as the position operator. The lecture covers the decomposition of wave functions into eigenstates, the calculation of probabilities associated with measurements, and the significance of normalization. The instructor also introduces the concept of averages over many measurements and the uncertainty principle, highlighting the limitations of classical determinism in quantum mechanics. The discussion includes practical examples, such as the behavior of polarized light and the implications of measurement on quantum states. The lecture concludes with an exploration of mixed states and the mathematical framework of projectors in quantum mechanics, emphasizing the importance of understanding the probabilistic nature of quantum systems.

Instructor

Pierre-André Besse

Teaching & PhD Past EPFL PhD Students Klaus Ehrmann Courses La science quantique : une vision singulière MICRO-444 Students understand the characteristics of quantum science. They master the formalism and use it in basic quantum systems: quantum wells, wires, dots or qubits. Physics of semiconductors devices MICRO-312 The students are able to explain the physics of semiconductor devices like diodes, transistors, and MOS devices. They use such devices in fundamental electroni

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Related concepts (32)

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.

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.

Quantum state

In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system. Quantum states may be defined in different ways for different kinds of systems or problems.

Quantum information

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields.

Interpretations of quantum mechanics

An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.

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