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Lecture

Mach-Zehnder Interferometer

In course

COM-309: Introduction to quantum information processing

Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prio ...

Description

This lecture covers the Mach-Zehnder interferometer, explaining the principle of superposition and the measurement postulate. It delves into density matrices, local operations, and experimental setups, discussing the classification of states and the detection probabilities.

Instructor

Nicolas Macris

Nicolas Macris received the PhD degree in theoretical physics from EPFL and then pursued his scientific activity at the mathematics department of Rutgers University (NJ, USA). He then joined the Faculty of Basic Science of EPFL, working in the field of quantum statistical mechanics and mathematical aspects of the quantum Hall effect. Since 2005 he is with the Communication Theories Laboratory and Information Processing group of the School of Communication and Computer Science and currently works at the interface of statistical mechanics, information theory and error correcting codes, inference and learning theory. He held long-term visiting appointments and collaborations with the University College and the Institute of Advanced studies in Dublin, the Ecole Normale Supérieure de Lyon, the Centre de Physique Theorique Luminy Marseille, Paris XI Orsay, the ETH Zürich and more recently Los Alamos National Lab. CV and publication list.

Official source

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.

Density matrix

In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states.

Quantum superposition

Quantum superposition is a fundamental principle of quantum mechanics. In classical mechanics, things like position or momentum are always well-defined. We may not know what they are at any given time, but that is an issue of our understanding and not the physical system. In quantum mechanics, a particle can be in a superposition of different states. However, a measurement always finds it in one state, but before and after the measurement, it interacts in ways that can only be explained by having a superposition of different states.

Random matrix

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice. In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms.

Pauli matrices

In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian, involutory and unitary. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted by tau (τ) when used in connection with isospin symmetries. These matrices are named after the physicist Wolfgang Pauli. In quantum mechanics, they occur in the Pauli equation which takes into account the interaction of the spin of a particle with an external electromagnetic field.

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