Editing Bell state (section)

{{Short description|Quantum states of two qubits}}

{{Quantum mechanics}}
In [[quantum information science]], the '''Bell's states''' or '''EPR pairs''' are specific [[quantum states]] of two [[qubits]] that represent the simplest examples of [[quantum entanglement]].<ref name="Nielsen-2010"/>{{rp|25}} The Bell's states are a form of entangled and [[unit vector|normalized]] [[basis vector]]s. This normalization implies that the overall probability of the particles being in one of the mentioned states is 1: <math>\langle \Phi|\Phi \rangle = 1</math>. Entanglement is a basis-independent result of [[Superposition principle|superposition]].<ref name="Sych-2009">{{Cite journal|last=Sych|first=Denis|date=7 January 2009|title=A Complete Basis of Generalized Bell States|journal=New Journal of Physics|volume=11|issue=1|page=013006|doi=10.1088/1367-2630/11/1/013006|bibcode=2009NJPh...11a3006S|via=IOP Science|doi-access=free}}</ref> Due to this superposition, measurement of the qubit will "[[Wave function collapse|collapse]]" it into one of its basis states with a given probability.<ref name="Nielsen-2010" /> Because of the entanglement, measurement of one qubit will "collapse" the other qubit to a state whose measurement will yield one of two possible values, where the value depends on which Bell's state the two qubits are in initially.  Bell's states can be generalized to certain quantum states of multi-qubit systems, such as the [[Greenberger–Horne–Zeilinger state|GHZ state]] for three or more subsystems.

Understanding of Bell's states is useful in analysis of quantum communication, such as [[superdense coding]] and [[quantum teleportation]].<ref>{{Cite journal|last1=Zaman|first1=Fakhar|last2=Jeong|first2=Youngmin|date=2 October 2018|title=Counterfactual Bell-State Analysis|doi=10.1038/s41598-018-32928-8 |journal=Scientific Reports|volume=8|issue=1|page=14641|pmid=30279547|pmc=6168595|bibcode=2018NatSR...814641Z|doi-access=free}}</ref> These mechanisms cannot transmit [[information]] faster than the speed of light, a result known as the [[no-communication theorem]].<ref name="Peres-2004">{{Cite journal |last=Peres |first=Asher |last2=Terno |first2=Daniel R. |date=2004-01-06 |title=Quantum information and relativity theory |url=https://link.aps.org/doi/10.1103/RevModPhys.76.93 |journal=Reviews of Modern Physics |language=en |volume=76 |issue=1 |pages=93–123 |arxiv=quant-ph/0212023 |bibcode=2004RvMP...76...93P |doi=10.1103/RevModPhys.76.93 |issn=0034-6861 |s2cid=7481797}}</ref>{{rp|100}}