Entanglement
of Quantum States| Entanglement
of Quantum States |
In General > s.a. correlations; quantum
experiments and foundations; phenomenology
of entanglement;
uncertainty.
* Idea: A linking that
persists between the wave functions of particles (photons, ions) even when
isolated from one another; Two subsystems
are entangled
if the total wave function is not factorizable, and values cannot
be assigned to observables for the individual systems; 2007, a notion of generalized
entanglement has emerged, defined through expectation values of preferred observables,
without reference to a subsystem decomposition.
* History: 2000, Long
the subject of discussion by philosophers of quantum theory, 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, entanglement sudden death observed [@ news pw(07)may].
* 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 qp/02-in;
Eisert & Plenio IJQI(03)qp [continuous
variables]; 4
· Horodecki RMP(09)qp/07;
Bengtsson & Zyczkowski 06; Silverman 08; Koh a0902;
Albert & Galchen SA(09)mar; Kanmani a0907.
@ General references: Corwin AJP(84)apr;
Zyczkowski PRA(99)
[volume]; Brukner et al qp/01;
Kauffman & Lomonaco NJP(02)qp [quantum
vs topological]; Terhal qp/03-in
['monogamy']; Viola et al qp/04-in
[for
sets of observables]; Kirkpatrick qp/04 [interpretation];
Shih a0706 [conceptual].
@ Subsystem-independent:
Barnum et al qp/03,
Viola & Barnum qp/07-in
[based
on observables].
@ Related 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;
Verstraete et al PRL(04)qp/03 [vs
correlations];
Ghirardi & Marinatto PRA(04)qp [and
indistinguishability], O&S(05)qp [identical
particles, criteria]; Hewitt-Horsman & Vedral PRA(07)qp/06
[in
Heisenberg picture]; Vedral JMO-qp/07
[from
higher-dimensional classical correlations]; Naudts & Verhulst PRA(07)
[ensemble-averaged]; Marek et al PRA(09)-a0705 [and non-classicality]; Arveson CMP(09)
[almost-surely entangled states].
@ And non-locality:
Methot & Scarani QIC(07)qp/06;
Barrett et al PRL(06)qp [maximally
entangled states]; Koashi et al a0709;
Giraud et al a0907.
Measures of Entanglement > s.a. entropy
in quantum mechanics; examples
of entangled systems.
* Idea: Two approaches
to entanglement measures are a geometric one and one based on fidelity;
The standard entanglement measure for a pure state is sin2
,
where is the angle
between the state and the closest separable one.
@ Reviews: Bruß JMP(02); Myhr qp/04-ms;
Plenio & Virmani QIC(07)qp/05.
@ General references: Popescu & Rohrlich PRA(97)qp/96 [entropy];
Schulman & Mozyrsky qp/97;
Vedral et al PRL(97)qp;
Nielsen PRL(99)qp/98 [partial
order]; Virmani & Plenio PLA(00)qp/99;
Rudolph JMP(01)mp/00;
Blanchard et al JPA(01)
[decoherence-based]; Majewski qp/01-in;
Zyczkowski & Bengtsson AP(02)qp/01;
Eisert et al JPA(02)qp/01 [infinite-dimensional
systems]; Vidal & Werner PRA(02)
[computable]; Nagel & Raggio qp/03;
Partovi PRL(04)qp/03;
Yukalov PRL(03)qp [as
operator action]; Christandl & Winter JMP(04);
Cavalcanti et al PRA(05)qp [maximal
entanglement and purity]; Mintert et al PRP(05)qp
[and dynamics]; Pawlowski & Czachor PRA(06)qp/05 [ambiguity,
photon]; Datta et al PRA(07)qp/06 [bounds];
Mintert & Buchleitner PRL(07)
[for mixed states]; Ostapchuk et al a0707 [interpretation];
Gour & Roy a0711;
Yang et al PRL(08)
[conditional entanglement of mutual information]; Sperling & Vogel a0908 [Schmidt
number]; Walborn PRL(09)
[entropic entanglement criteria]; Ma & Zhang a0910 [D-concurrence];
Streltsov a0911 [comparison].
@ Geometric: Blasone et al PRA(08)-a0712; Uyanik
& Turgut a0910.
@ Experimental: Gühne et al PRL(07)qp/06 [estimate];
Kothe & Björk PRA(07)qp/06 [through
local observable correlations]; Badziag et al PRL(08)
[experimentally friendly sufficient conditions]; Zhang et al PRA(08)-a0806 [for
mixed states].
@ Uniqueness: Rudolph JMP(01)qp;
Donald et al JMP(02)qp/01.
@ Multipartite: Eisert & Briegel PRA(01)qp/00;
Meyer & Wallach qp/01;
Miyake PRA(03);
Heydari & Björk JPA(04)qp/04;
Pitowsky qp/06-wd
[entanglement classes]; Adesso et al PRA(07)qp/06;
Facchi et al IJQI(07)qp/06;
Cardy a0708-in
[and von Neumann entropy]; Facchi et al a0803 [statistical
mechanics]; Teresi et al a0805;
Hassan & Joag a0901;
Hilling & Sudbery a0905 [geometric
measure of entanglement]; Osterloh & Hyllus a0908 [estimate].
Other References > s.a. geometric
phase; hidden variables; phase
transition;
wigner functions.
@ And information theory: 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).
@ Limits to entanglement: Gambini et al PLA(08)-a0708 [from
use of realistic rods].
@ Multiscale entanglement renormalization ansatz: Cincio et al PRL(08) [2D
Ising model].
@ Geometry: Kus & Zyczkowski PRA(01);
Bertlmann et al PRA(02)qp/01;
Lévay JPA(04)qp/03;
Leinaas et al PRA(06)qp;
Zyczkowski & Bengtsson in(06)qp [intro];
Sugita a0704-in
[and topological links]; Basu & Bandyopadhyay IJGMP(07)
[and geometric phase]; Cavalcanti et al a0709 [and geometry of set of quantum
states].
@ Thermodynamics: Horodecki et al PRL(02);
Korbicz et al JPA(08)-a0704;
Vedral a0706 [dissipative
systems]; Brandão & Plenio Nat(08)-a0810 [and
the second law]; > s.a. quantum
statistical mechanics.
@ Classical analog: Spreeuw FP(98); Massar et al PRA(01)qp/00;
Lakshminarayan qp/01;
Collins & Popescu PRA(02)qp/01.
@ Conceptual: Esfeld SHPMP(04) [and metaphysics of relations].
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nov
2009