"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."
Discussion of the phenomenon of quantum entanglement, as well as its potential use for quantum teleportation and communication.
Quantum mechanics: The branch of physics that studies the behavior of matter and energy at the quantum level.
Superposition: The ability of a quantum system to exist in multiple states at the same time.
Entanglement: The phenomenon where two or more quantum systems become inexplicably interconnected and share a single quantum state.
Bell's inequality: A mathematical theorem that demonstrates the incompatibility of certain predictions of classical physics with the predictions of quantum mechanics.
Bell test: A series of experiments designed to test the validity of Bell's inequality and confirm the reality of quantum entanglement.
Non-locality: The concept that quantum entanglement allows for instantaneous communication and action at a distance, seemingly violating the limitations of relativity.
Quantum teleportation: The process of transferring quantum information from one location to another, using entanglement to "teleport" the state of one particle onto another.
Quantum information theory: The study of how information is processed and transmitted using quantum systems, including encryption, decoding, and transmission.
Quantum cryptography: The use of quantum principles to secure communication and encryption, with protocols that exploit the properties of entanglement and superposition.
Quantum computing: The use of quantum systems to perform calculations and computations faster than classical computers, using the principles of superposition and entanglement to create exponentially more powerful algorithms.
Pure-state entanglement: A state where two or more subsystems are entangled and cannot be expressed individually.
Mixed-state entanglement: A state where a subsystem is entangled with the environment, creating a mixed state.
Entanglement swapping: A process where entanglement is transferred from one system to another via a third entangled system.
Entanglement distillation: A process where the entanglement of two mixed-state entangled systems is increased.
Quantum teleportation: A process where the quantum state of a particle is transferred from one location to another without physically moving the particle.
Quantum key distribution: A method for secure communication using entangled particles to ensure that the communication cannot be intercepted or tampered with.
Coherent feedback network: A process where entangled particles are used to create a feedback loop, allowing for the transfer of quantum information between distant locations.
Remote state preparation: A process where the state of a quantum particle is prepared in one location and sent to another location using entangled particles.
Teleportation of quantum gates: A process where a quantum gate is teleported from one system to another using entangled particles.
"Entanglement is a primary feature of quantum mechanics not present in classical mechanics."
"Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated."
"Any measurement of a particle's properties results in an apparent and irreversible wave function collapse of that particle and changes the original quantum state."
"Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter."
"Einstein and others considered such behavior impossible, as it violated the local realism view of causality (Einstein referring to it as 'spooky action at a distance') and argued that the accepted formulation of quantum mechanics must therefore be incomplete."
"The counterintuitive predictions of quantum mechanics were verified in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating Bell's inequality."
"In earlier tests, it could not be ruled out that the result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location. However, so-called 'loophole-free' Bell tests have since been performed where the locations were sufficiently separated that communications at the speed of light would have taken longer—in one case, 10,000 times longer—than the interval between the measurements."
"According to some interpretations of quantum mechanics, the effect of one measurement occurs instantly."
"Other interpretations which do not recognize wavefunction collapse dispute that there is any 'effect' at all."
"Despite popular thought to the contrary, quantum entanglement cannot be used for faster-than-light communication."
"On 14 August 2023, researchers reported the first-ever image of quantum entanglement." Note: Some questions might require the synthesis of information from multiple parts of the paragraph.