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Quantum entanglement is the phenomenon in which the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance.

The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: 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. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. This behavior gives rise to seemingly paradoxical effects: 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. With entangled particles, such measurements affect the entangled system as a whole. Einstein and others considered such behavior impossible, as it violated the local realism view of causality and argued that the accepted formulation of quantum mechanics must therefore be incomplete. Later, 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. This established that the correlations produced from quantum entanglement cannot be explained in terms of local hidden variables. Entanglement can produce statistical correlations between events in widely separated places, but it cannot be used for faster-than-light communication. Quantum entanglement has been demonstrated experimentally with photons, electrons, top quarks, molecules and even small diamonds. The use of quantum entanglement in communication and computation is an active area of research and development.

That same year, Hermann Weyl observed in his textbook on group theory and quantum mechanics that quantum systems composed of multiple interacting parts exhibit a kind of Gestalt, in which "the whole is greater than the sum of its parts". In 1932, Erwin Schrödinger derived the defining equations of quantum entanglement but left them unpublished. Schrödinger followed up with a full paper defining and discussing the notion of entanglement, saying "I would not call one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought." Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity. Beginning in the mid-1990s, Anton Zeilinger used the generation of entanglement via parametric down-conversion to develop entanglement swapping and demonstrate quantum cryptography with entangled photons.

This illustrates how multipartite entanglement is a more complicated topic than bipartite entanglement: systems composed of three or more parts can exhibit multiple qualitatively different types of entanglement.

Entanglement measures quantify the amount of entanglement in a (often viewed as a bipartite) quantum state. As aforementioned, entanglement entropy is the standard measure of entanglement for pure states (but no longer a measure of entanglement for mixed states).

Most (but not all) of these entanglement measures reduce for pure states to entanglement entropy, and are difficult (NP-hard) to compute for mixed states as the dimension of the entangled system grows.

Entanglement has many applications in quantum information theory. Entanglement is used in some protocols of quantum cryptography, but to prove the security of quantum key distribution (QKD) under standard assumptions does not require entanglement; however, the device independent security of QKD is shown exploiting entanglement between the communication partners.

It is also possible to create entanglement between quantum systems that never directly interacted, through the use of entanglement swapping.

Quick Facts

• The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
• Entanglement is used in some protocols of quantum cryptography, but to prove the security of quantum key distribution (QKD) under standard assumptions does not require entanglement; however, the device independent security of QKD is shown exploiting entanglement between the communication partners.
• This established that the correlations produced from quantum entanglement cannot be explained in terms of local hidden variables.
• As aforementioned, entanglement entropy is the standard measure of entanglement for pure states (but no longer a measure of entanglement for mixed states).
• That same year, Hermann Weyl observed in his textbook on group theory and quantum mechanics that quantum systems composed of multiple interacting parts exhibit a kind of Gestalt, in which "the whole is greater than the sum of its parts".

Source material: Wikipedia - "Quantum entanglement". Adapted and summarized for DiscoverScroll. Original contributors are credited through the linked Wikipedia article. Read original on Wikipedia. CC BY-SA 4.0. Changes were made from the original.