Examples of Entangled Systems and States| 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 JHEP(15)-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;
> s.a. coherent states.
@ 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];
Fukuda & König JMP(19)-a1903.
@ 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 [dynamics, effects, observation].
@ 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];
Datta et al EPJD(18)-a1705 [3, pure states];
Samuel et al AP(18)-a1801 [2];
Chen & Jiang a1901 [hierarchy of entanglement criteria];
Yang et al CTP(19)-a1906 [monogamy and polygamy inequalities of multiqubit entanglement];
> s.a. phenomenology; quantum computing.
@ 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];
Kuś et al a1811 [large angular momenta].
@ 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 Quant(19)-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];
Pappalardi et al PRB(18)-a1806 [long-range 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, spacetime]; 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];
Merdaci & Jellal PLA-a1909 [three coupled harmonic oscillators].
@ 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 nComm(17)-a1702 [wave-particle entanglement of two photons];
news cosmos(17)oct [satellites around earth];
news pt(18)nov [trio of entangled qutrits].
@ 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];
Barros et al a1912 [role of particle indistinguishability].
@ 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];
Cornfeld et al PRA(19)-a1808 [experimental setups];
Shi et al a1906 [in accelerated frames].
@ 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];
news cosmos(18)apr;
Marletto et al JPcomm(18)
[Coles et al Small(17)]
+ news livesci(18)nov [between living bacteria].
@ 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 PRP(16)-a1512 [rev];
> s.a. entanglement entropy [spin chains].
@ 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 sRep-a1508 [multiphoton];
Pichler et al PRX(16) [cold atoms, measurement protocol];
Alba et al JSM(19)-a1807 [random inhomogeneous systems, area-law violations];
Bertini et al PRX(19) [chaotic quantum systems].
@ 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].
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