Examples of Entangled Systems and States  

Types of States > s.a. composite systems; entanglement [including status].
@ Types of entanglement: Krenn & Zeilinger PRA(96) [non-objective]; Popp et al PRA(05)qp/04 [localizable]; Buniy & Kephart JPA(12)-a1012, JPA(12) [algebraic classification].
@ For superpositions: Gour PRA(07)-a0707 [tight lower and upper bounds].
@ For mixed states: Giannetto in(95) [entanglement requires a density matrix]; Mintert & Buchleitner PRL(07); Bhardwaj & Ravishankar qp/07; Qi & Hou a1010 [from density-matrix entries]; Eltschka & Siewert PRL(12)-a1304 [3-qubit states]; Hsiang & Hu a1503 [at high temperatures].
@ And coherent states: Wang & Sanders PRA(02)qp/01 [multipartite]; Clausen et al PRA(02)qp; Barnum et al PRA(03)qp/02.
@ Gaussian states: Adesso PRL(06)qp [N-mode, pure]; Anders qp/06-dipl [bipartite]; Adesso PhD-qp/07; Adesso & Illuminati PRA(08)-a0805; Buono et al JOSA(10)-a1006 [bipartite]; Chaitanya et al a1501 [multi-mode Gaussian states].
@ Gaussian states, entanglement of formation: Ivan & Simon a0808; Marian & Marian PRL(08)-a0809; Nicacio & de Oliveira PRA(14)-a1310.
@ Other types of states: Stenholm FP(09) [pure states]; Namiki JPSJ(10)-a0906 [non-Gaussian]; Hajdusek & Vedral NJP(10)-a0911 [cluster states].

Simple Systems > s.a. brownian motion; cellular automaton; lattice theories; networks; phenomenology of entanglement.
@ Qubits: Wootters PRL(98)qp/97 [2]; van Enk PRA(05)qp [|0\(\rangle\)|1\(\rangle\) + |1\(\rangle\)|0\(\rangle\)]; Avron & Kenneth AP(09) [2]; Cui et al JPA(09) [2 coupled, in a common environment]; Gour & Wallach JMP(10)-a1006 [4]; Aulbach et al LNCC(10)-a1010, Aulbach a1103-conf [n, symmetric entanglement classes]; El-Orany a1106, a1204 [2, spin-correlation matrix]; de Vicente et al PRL(12)-a1106 [3, operational measures]; Tian et al AP(13)-a1301 [2 and 3, one accelerated]; Borsten JPCS(14)-a1311 [3, using Jordan algebras]; Holweck et al JMP(14) [4]; Banerjee et al a1504 [n, maximal entanglement concentration]; Rangamani & Rota JPA(15)-a1505 [detailed analysis of entanglement structures]; Samuel et al a1801 [2]; > s.a. phenomenology.
@ Chains, graph states: Wootters CM(02)qp/00; Hein et al PRA(04); Han & Duan a0708-wd; Van den Nest et al PRA(08); Cabello et al PRA(09)-a0904 [invariants for 8 qubits]; Collins et al JPA(10)-a1003 [random graph states]; Ivanchenko a1106 [qutrit chain in a magnetic field]; Wu et al PRA(14)-a1403 [randomized graph states]; > s.a. Quantiki page.
@ Single-particle systems: Can et al qp/04/JOB; Terra Cunha et al PRS(07)qp/06 [atom]; Dasenbrook et al NJP(16)-a1511 [electron]; > s.a. neutrino oscillations.
@ Two-particle systems: Curilef et al EJP(06) [in a double well, speed of evolution]; Castro-Ruiz & Nahmad-Achar PRA(12)-a1210 [spin-1, and Lorentz transformations]; Man'ko & Markovich JRLR(15)-a1406 [spin-1/2]; Mihaescu & Isar RJP-a1512 [two bosonic modes in a thermal environment]; Karczewski & Kurzyński PRA(16)-a1608 [distinguishable].
@ Atoms: Tommasini et al AJP(98)oct-qp/97, Zhu et al PhyA(05) [e-p in H]; Turchette et al PRL(98) + pn(98)nov; Sackett et al Nat(00)mar [ions]; Lombardi & Matzkin PRA(06)qp [molecules]; Moehring et al Nat(07)sep + pw(07)sep [1 m apart]; Vacanti & Beige NJP(09)-a0903 [preparation]; Jost et al Nat(09)jun-a0901 + news BBC(09)jun [motions of pairs of atoms]; Sancho & Plaja JPB(09) [unstable atoms, modified emission properties]; Rossatto & Villas-Boas PRA(13)-a1307 [two atoms in a cavity]; news sn(17)mr [millions of atoms].
@ Atom + photon: Inoue et al PRA(06)qp; de Riedmatten et al PRL(06)qp; Rosenfeld et al PRL(08).
@ 3-way: Schlienz & Mahler PLA(96) [three 2-level systems, maximally entangled]; Coffman et al PRA(00)qp/99 [distributed]; Carteret et al FP(99); Fivel FP(99); & GHZ, Seevinck & Uffink PRA(02) [3 particles]; Eisert & Gross qp/05-ch; Low et al qp/06 [collisional decoherence and rarity of entanglement]; Yu & Song PRA(06)qp [tripartite, criterion]; Boixo & Monras PRL(08)-a0706 [operational interpretation]; Sabín & García-Alcaine EPJD(08)-a0707 [3 qubits]; Facchi et al PRA(09)-a0908 [maximally entangled]; Park & Lee IJTP(12)-a1012 [separable states and entanglement distribution]; Buscemi & Bordone PRA(11) [tripartite, for bosons or fermions].
@ Multipartite: Iwai JPA(07) [multi-qubit]; Huber et al PRL(10); Band & Osherov a1010; Grabowski et al JPA(11)-a1012 [in terms of representation theory of symmetry groups]; Schwemmer et al PRL(15)-a1410 [without multipartite correlations]; Miklin et al PRA(16)-a1506 [as an emergent phenomenon]; Patrascu JHEP(17)-a1707 [and topology]; Bryan et al a1801 [locally maximally entangled states].
@ Spin systems: Schliemann PRA(03) [SU(2)-invariant]; Calsamiglia et al qp/05 [spin gas]; Novaes AP(05) [two interacting spins in constant B]; Campos Venuti et al PRL(06)qp [long-range]; Tribedi & Bose PRA(06)qp [spin clusters]; Verhulst & Naudts JPA(07) [microcanonical ensemble]; Saguia et al PRA(07)qp [random spin chains]; Botero & Reznik a0708 [scaling and universality at criticality]; Latorre & Riera JPA(09)-a0906 [rev]; Dudin et al PRL(09) [photon + optical-lattice spin wave]; Ng & Bose JPA(10) [stability]; Galve et al EPJST(10)-a1004 [far from equilibrium]; Zheng et al PRA(10)-a1005 [between blocks of spins]; Zenchuk a1005 [homogeneous spin-1/2 chains]; Simmons et al Nat(11)feb-a1010 [solid-state spin ensemble]; Esfahani JPA(10)-a1010 [spin-1/2 particles in a gravitational field]; Cattaruzza et al PLA(14)-a1308 [supersymmetric quantum mechanics]; Torlai et al JSM(14)-a1311 [dynamics of the entanglement spectrum]; Cui & Mintert NJP(15)-a1407 [disordered spin chains]; > s.a. ising model; spin models [Heisenberg models].
@ Other simple systems: Sassoli de Bianchi AP(13)-a1301 [two dice]; > s.a. particle statistics [identical particles]; quantum systems.

Other Systems > s.a. entanglement in quantum field theory [including cosmology]; topology and physics [non-trivial topologies].
* Photons: A standard way to obtain entanglement is through double emission of photons by an excited atom; > s.a. optics [classical]; photon phenomenology.
@ Oscillators: Paz & Roncaglia PRL(08)-a0801, PRA(09)-a0809, Isar PS(11)-a1102, Queisser et al a1111 [two in a common environment]; Miao et al PRA(10) [and continuous field].
@ Photons: Poh et al PRL(15) + news as(15)nov [close to the Tsirelson bound]; Hiesmayr et al PRL(16) [4]; Wang et al PRL(16) [10]; Rab et al a1702 [wave-particle entanglement of two photons]; news cosmos(17)oct [satellites around earth].
@ Other bosons: Paskauskas & You PRA(01)qp [2 bosons]; Sarkar FP(10)-a0907 [neutral kaons, CPT, and spacetime foam]; Wang et al JPA(06)qp, Dalton et al a1506 [identical bosons].
@ Fermions: Schliemann et al PRB(01); Zanardi PRA(02)qp/01; Kaplan FNL(05)qp; Finster JPA(10)-a0911 [and fermionic projector]; Grover PRL(13)-a1307 [interacting, in Monte Carlo simulations]; Ladyman et al SHPMP(13) [and non-factorizability]; Benatti et al PRA(14)-a1403; Valdés-Hernández et al PRA(15)-a1501 [systems of identical fermions undergoing decoherence]; Sokoli & Kümmerer a1507 [identical particles]; Gigena & Rossignoli PRA-a1509; Benatti & Floreanini JPA(16)-a1605 [in algebraic quantum mechanics].
@ Open systems: Hartmann et al NJP(07); Isar PS(09)-a0812-conf.
@ Macroscopic systems: Julsgaard et al Nat(01)qp + pn(01)sep [gas, long-lived]; Shimizu & Morimae PRL(05)qp; news pw(13)oct [tiny mechanical drum and microwave field]; Ghobadi et al PRL(14)-a1401 + news PhysOrg(14)apr, Wang et al PRA(15)-a1412 [micro-macro entangled states (and quantum gravity)]; Schnabel PRA(15) + news pw(15)aug [two 100-g mirror proposal]; Tiranov et al PRL(16)-a1510 [micro-macro entanglement between a photon and many atoms].
@ Condensed-matter systems: Brukner et al PRA(06)qp/04 [antiferromagnetic spin chains]; Dowling et al PRA(06)qp; Skrøvseth PhD(06)qp; Osterloch Hab(07)-a0810; Cramer et al PRL(11)-a1009 [and measurement]; news pw(11)dec [two diamonds 15 cm apart]; Fogarty et al PRA(13)-a1208 [two defects embedded in a crystalline structure]; Schuch a1306-ln [rev, esp tensor network states]; Forgues et al PRL(15) [quantum conductor at low temperatures]; Laflorencie a1512 [rev].
@ Many-body systems: Amico et al RMP(08)qp/07; Clark et al FP(10); Cirac a1205-proc [quantum-information perspective]; Abanin & Demler PRL(12), Daley et al PRL(12) [experiments, measurement]; Eisert a1308-ln [and tensor network states]; Bardarson et al PRL(12), Nanduri et al PRB(14)-a1404 [entanglement spreading]; Boette et al PRB(15)-a1410 [mean-field description]; Cianciaruso et al a1412 [and quantum correlations]; Ho & Abanin PRB(17)-a1508; He et al a1508 [multiphoton]; Pichler et al PRX(16) [cold atoms, measurement protocol].
@ Systems that never interacted: Guerra & Carvalho JMO(06)qp/05 [atoms]; Sabín et al PRL(12)-a1202 + news PhysOrg(12)jul [qubits, past-future entanglement].
@ Other systems: Nienhuis JPA(01) [decay]; Braun PRA(05) [heat-bath-induced entanglement]; Harshman QIC(07)qp/06 [continuous-discrete]; Adesso & Illuminati JPA(07)qp [continuous-variable systems]; Bastidas et al PRA(10)-a0910 [driven, and parametric resonance]; Lee & Vidal PRA(13)-a1306 [topologically ordered systems, entanglement negativity]; Bellomo & Antezza NJP(13)-a1310 [systems out of thermal equilibrium].

main pageabbreviationsjournalscommentsother sitesacknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 11 jan 2018