Entanglement of Quantum States| 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.
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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