Lecture

Quantum Density Matrix Formalism

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In course

PHYS-314: Quantum physics II

The aim of this course is to familiarize the student with the concepts, methods and consequences of quantum physics. ...

Description

This lecture covers the formalism of quantum density matrices, including topics such as density matrix representation, properties, and applications in quantum mechanics. The instructor explains the concept of density matrices in quantum physics and their significance in describing mixed states and quantum operations.

Instructors (3)

Vincenzo Savona

Vincenzo Savona studied physics in Pisa at the Scuola Normale Superiore and the University of Pisa, prior to completing his PhD at the EPFL's Institute of Theoretical Physics. Subsequently he did post-doctoral work, first at the EPFL and then in the physics department of the Humboldt University of Berlin. In 2002, he returned to the EPFL to create his own research group, receiving a "professeur boursier" fellowship from the Swiss National Science Foundation. In 2006, he was appointed tenure-track assistant professor at the EPFL and joined the NCCR for Quantum Photonics. In 2010 he was appointed associate professor. Currently he directs the Laboratory of Theoretical Physics of Nanosystems.

Florent Gérard Krzakala

Zoë Holmes

Teaching & PhD PhD Students Ricard Puig, Sacha Lerch, Reyhaneh Aghaei Saem, Shao Hen Chiew, Weijie Xiong, Marc Sanz Drudis, Mehrad Sahebi, Manuel Rudolph Courses Quantum information theory PHYS-550 After recapping the basics of quantum theory from an informationtheoretic perspective, we will cover more advanced topics inquantum information theory. This includes introducing measures of quantum information, and developing a more advanced understanding quantum states, channels and measurement

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

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.

Von Neumann entropy

In physics, the von Neumann entropy, named after John von Neumann, is an extension of the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics. For a quantum-mechanical system described by a density matrix ρ, the von Neumann entropy is where denotes the trace and ln denotes the (natural) matrix logarithm. If the density matrix ρ is written in a basis of its eigenvectors as then the von Neumann entropy is merely In this form, S can be seen as the information theoretic Shannon entropy.

Quantum operation

In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan. The quantum operation formalism describes not only unitary time evolution or symmetry transformations of isolated systems, but also the effects of measurement and transient interactions with an environment.

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

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