Entanglement of Quantum States  

In General > s.a. Coherence; correlations; quantum experiments and foundations; types of quantum states [separable].
* Idea: One of various quantities used to characterize non-local, stronger-than-classical correlations in quantum systems, even when isolated from one another; Two subsystems are entangled if the total wave function is not factorizable, which means that values cannot be assigned to a complete set of observables for each individual system; It is the "spooky action at a distance" that disturbed Einstein so much.
* History: 1935, Concept of "Verschränkung" introduced by E Schrödinger when physicists were debating the EPR paradox; 2000, Long the subject of discussion by philosophers of quantum theory, it has recently come to play an essential role for physicists in their development of quantum information theory; Entangled state of 4 particles, and between Be atoms achieved; 2001, Entangled state of two trillion-atom gas clouds achieved; 2003, Two solid-state superconducting qubits entangled over 0.7 mm (earlier only micron scale); 2003, Effects seen in the bulk properties of a magnetic salt crystal [@ news pw(03)sep]; 2004, 3- and 4-photon entanglement produced, beating the diffraction limit [@ news pw(04)may]; 2005, Entangled states of 6 Be atoms and 8 Ca atoms [@ news pw(05)dec]; 2007, A notion of generalized entanglement has emerged, defined through expectation values of preferred observables, without reference to a subsystem decomposition; 2007, entanglement sudden death observed [@ news pw(07)may]; > s.a. history of quantum theory.
* Uses: It allows teleportation and quantum key distribution, which are impossible in the classical world; > s.a. entanglement phenomenology.
* And non-locality: It is often assumed that the most non-local states are the maximally entangled ones; This is not the case.
@ II: Kwiat & Hardy AJP(00)jan [quantum cakes]; Aczel 02; Terhal et al PT(03)apr; Adesso a0706 ["social aspects"].
@ Reviews, intros: Eckert et al in(03)qp/02; Eisert & Plenio IJQI(03)qp [continuous variables]; 4 · Horodecki RMP(09)qp/07; Bengtsson & Życzkowski 06; Silverman 08; Koh a0902; Albert & Galchen SA(09)mar; Kanmani a0907; Gabriel a1003-dipl; Orzel a1208/AJP [limits]; Walter et al a1612, Bengtsson & Życzkowski a1612-ch [multipartite]; in Chang & Ge 17; Schroeder AJP(17)nov-a1703 [pictorial examples]; Alsina a1706-PhD; Paneru et al RPP(20)-a1911; Gudder a2005.
@ General references: Corwin AJP(84)apr; Życzkowski PRA(99) [volume]; Brukner et al qp/01; Viola et al qp/04-proc [for sets of observables]; news sn(10)nov [loophole closed]; Li et al AMP(10)-a1012; Masanes et al JMP-a1111 [in more general theories]; Balachandran et al PRL(13)-a1205, PRD(13)-a1301 [algebraic approach, based on the GNS construction]; Aerts & Sozzo LNCS(14)-a1304; Aerts & Sassoli de Bianchi conf(16)-a1502 [and the extended Bloch representation]; de Ronde & Massri a1809 [logos categorical approach]; Gudder a1904 [general theory]; Cai et al a2006 [for any definition of subsystems].
@ Conceptual: Esfeld SHPMP(04) [and metaphysics of relations]; Shih a0706; Bokulich & Jaeger ed-10 [philosophy]; Sudbery AIP(11)-a1103 [philosophical lessons]; Hobson a1607 [meaning]; de Ronde & Massri a1808, a1911 [definition in non-collapse, no-small-particles interpretations].
@ Monogamy: Terhal IBM(04)qp/03-conf; Lancien et al PRL(16)-a1604; Raju a1809 [and violation of locality in quantum gravity].
@ And fluctuations: Song et al PRB(10)-a1002; Bhaumik a1411 [from inherent quantum fluctuations]; Frérot & Roscilde PRB(15)-a1506.
@ And correlations: Verstraete et al PRL(04)qp/03 [vs correlations]; Vedral JMO(07)qp [from higher-dimensional classical correlations]; Klobus et al EPJD(19)-a1808 [multipartite entanglement without multipartite correlations].
@ And non-locality: Methot & Scarani QIC(07)qp/06; Barrett et al PRL(06)qp [maximally entangled states]; Koashi et al a0709; Spengler et al JPA(11)-a0907 [in discrete systems]; Giraud et al a0907-proc; Mazzola et al PRA(10)-a1003 [entanglement, mixedness and non-locality]; Gillis FP(11)-a1007; Vallone et al PRA(14)-a1106 [non-locality and entanglement as opposite properties]; Buscemi PRL(12) + Massar & Pironio Phy(12)may [all entangled quantum states are non-local]; Kupczynski AIP(12)-a1205; Liang et al PRA(12); Schmid et al a2004; > s.a. XY Chain.
@ And topology: Kauffman & Lomonaco NJP(02)qp; Sugita a0704-proc [topological links]; Kauffman & Mehrotra a1611 [topological braiding].
@ For general probabilistic theories: Holik et al a1202 [informational invariance]; Aubrun et al a1910 [and state superposition]; > s.a. indefinite causal relations.
blue bullet Specific aspects: see phenomenology and measures of entanglement; entanglement in field theory and spacetime; examples of systems.

Related Topics > s.a. hidden variables; phase transitions; quantum statistical mechanics [entanglement thermodynamics]; wigner functions.
* Interpretation: In topological theories entanglement of subsystems can be given an intuitive interpretation in terms of "strings" connecting them; More generally, the density matrix of a mixed state can be represented by cobordisms of topological spaces.
@ Subsystem-independent: Barnum et al PRL(04)qp/03, Viola & Barnum qp/07-proc [based on observables].
@ And non-classicality: Marek et al PRA(09)-a0705; Ivan et al PRA(13)-a1306; Vogel & Sperling PRA(14)-a1401 [unified treatment]; Gholipour & Shahandeh PRA(16)-a1603 [entangled states of arbitrarily high temperature and number of particles].
@ Entanglement of formation: Li & Fei PRA(10)-a1010; de Oliveira et al PRA(14)-a1312 [monogamous].
@ Entanglement and information: Cerf & Adami PhyD(98)qp/96 [and measurement]; Plenio & Vedral CP(98)qp [rev]; Eisert PhD(01)qp/06; Macchiavello PhyA(04); Ainsworth FP(07).
@ Entanglement in time: Milz et al a2011 [multipartite]; Marletto et al a2103 [temporal teleportation and emergent dynamics]; Castellani a2104 [entropy].
@ Limits to entanglement: Gambini et al PLA(08)-a0708 [from use of realistic rods].
@ Geometry, interpretation: Kuś & Życzkowski PRA(01); Bertlmann et al PRA(02)qp/01; Lévay JPA(04)qp/03; Kirkpatrick qp/04 [interpretation]; Leinaas et al PRA(06)qp; Życzkowski & Bengtsson in(06)qp [intro]; Basu & Bandyopadhyay IJGMP(07) [and geometric phase]; Cavalcanti et al PRA(08)-a0709 [and geometry of the space of states]; Sawicki et al CMP(11)-a1007 [symplectic geometry]; Kiosses JPA(14)-a1403 [entanglement as pure spinor geometry, Cartan equation and Dirac spinors]; Boyer et al PRA(17)-a1608; Bej & Deb QIP(19)-a1805 [and geometry of the space of states]; Melnikov et al JHEP(19)-a1809 [topological]; > s.a. geometric phase.
@ Classical analog: Spreeuw FP(98); Massar et al PRA(01)qp/00; Lakshminarayan qp/01; Collins & Popescu PRA(02)qp/01; Solomon & Ho proc(10)-a1104 [topological and quantum entanglement]; Matzkin AIP(11)-a1110 [fate of entanglement for vanishing Planck constant]; Bharath & Ravishankar PRA(14)-a1401 [classical simulation]; Snoke a1406 [classical, macroscopic model]; Aiello et al NJP(15)-a1409; Fu & Wu a1502 [effective simulation]; D'Ariano et al PRA(20)-a1909.
@ Other topics: Schlienz & Mahler PRA(95); Lo & Popescu qp/97; Peres PS(98)qp/97; Yu Shi AdP(00)qp/98 [Gedankenexperiments]; D'Ariano et al PLA(00)qp [Bell measurements]; Ghirardi et al JSP(02)qp/01; Hewitt-Horsman & Vedral PRA(07)qp/06 [in the Heisenberg picture]; Naudts & Verhulst PRA(07) [ensemble-averaged]; Arveson CMP(09) [almost-surely entangled states]; de la Torre et al EJP(10)-a1002; Zanardi & Campos Venuti JSM(13)-a1205 [entanglement susceptibility]; Yamazaki EPL(13)-a1304 [in theory space]; Brandão & Cramer PRB(15)-a1409 [area law and specific heat]; Kollas a1603-MSc [thermodynamical structure]; Richens et al PRL(17)-a1705 + news gm(17)aug [and emergent classicality]; Liu et al JHEP(18)-a1807 [and state scrambling]; > s.a. uncertainty.

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