Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Quantum State Spaces: Pure vs Mixed States

In course

PHYS-550: Quantum information theory

After recapping the basics of quantum theory from an information theoretic perspective, we will cover more advanced topics in quantum information theory. This includes introducing measures of quantum information, and developing a more advanced understandin ...

Description

This lecture delves into the concept of quantum state spaces, comparing pure and mixed states, and explores ensemble decompositions. The instructor discusses the state space of a qubit, classical 2-level systems, and the importance of ensuring the purity of quantum systems.

Instructor

Zoë Holmes

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

Related concepts (32)

Qubit

In quantum computing, a qubit (ˈkjuːbɪt) or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization.

Flux qubit

In quantum computing, more specifically in superconducting quantum computing, flux qubits (also known as persistent current qubits) are micrometer sized loops of superconducting metal that is interrupted by a number of Josephson junctions. These devices function as quantum bits. The flux qubit was first proposed by Terry P. Orlando et al. at MIT in 1999 and fabricated shortly thereafter. During fabrication, the Josephson junction parameters are engineered so that a persistent current will flow continuously when an external magnetic flux is applied.

Phase qubit

In quantum computing, and more specifically in superconducting quantum computing, the phase qubit is a superconducting device based on the superconductor–insulator–superconductor (SIS) Josephson junction, designed to operate as a quantum bit, or qubit. The phase qubit is closely related, yet distinct from, the flux qubit and the charge qubit, which are also quantum bits implemented by superconducting devices.

Charge qubit

In quantum computing, a charge qubit (also known as Cooper-pair box) is a qubit whose basis states are charge states (i.e. states which represent the presence or absence of excess Cooper pairs in the island). In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island coupled by a Josephson junction (or practically, superconducting tunnel junction) to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs that have tunneled across the junction.

Superconducting quantum computing

Superconducting quantum computing is a branch of solid state quantum computing that implements superconducting electronic circuits using superconducting qubits as artificial atoms, or quantum dots. For superconducting qubits, the two logic states are the ground state and the excited state, denoted respectively. Research in superconducting quantum computing is conducted by companies such as Google, IBM, IMEC, BBN Technologies, Rigetti, and Intel. Many recently developed QPUs (quantum processing units, or quantum chips) utilize superconducting architecture.

Related lectures (60)

Quantum Random Number Generation

Explores quantum random number generation, discussing the challenges and implementations of generating good randomness using quantum devices.

Quantum Qubits: Understanding the Basics

Covers the basics of quantum qubits, including abstract qubits, states, measurement, and evolution in quantum computation.

Quantum Computing Basics

Covers the basics of quantum computing, focusing on superconducting qubits, scaling challenges, and potential applications.

Superconducting Qubits: Circuit QED Technology

Explores superconducting qubits and circuit quantum electrodynamics technology, discussing relaxation, dephasing, environmental noise, and material defects.

Quantum Measurements