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Lecture

Entanglement: Bell States

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 notion of entanglement, dense coding, teleportation, Bell inequality, and its application to Quantum Key Distribution. It explains the concept of entangled states with two parties, including product states and entangled states.

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

Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

Related concepts (31)

Quantum teleportation

Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation is commonly portrayed in science fiction as a means to transfer physical objects from one location to the next, quantum teleportation only transfers quantum information. The sender does not have to know the particular quantum state being transferred. Moreover, the location of the recipient can be unknown, but to complete the quantum teleportation, classical information needs to be sent from sender to receiver.

Bell state

The Bell's states or EPR pairs are specific quantum states of two qubits that represent the simplest examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell's states are a form of entangled and normalized basis vectors. This normalization implies that the overall probability of the particle being in one of the mentioned states is 1: . Entanglement is a basis-independent result of superposition.

Quantum entanglement

Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.

No-teleportation theorem

In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits (or even an infinite number of such bits); nor can such bits be used to reconstruct the original state, thus "teleporting" it by merely moving classical bits around. Put another way, it states that the unit of quantum information, the qubit, cannot be exactly, precisely converted into classical information bits.

Superdense coding

In quantum information theory, superdense coding (also referred to as dense coding) is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource. In its simplest form, the protocol involves two parties, often referred to as Alice and Bob in this context, which share a pair of maximally entangled qubits, and allows Alice to transmit two bits (i.e.

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