Quantum
Correlations |

**In General** > s.a. bell inequalities
and generalizations [and causal networks]; correlations
[quantumness measures]; fluctuations; types and bounds.

* __Rem__: Understanding the nature
of correlations among distant observables is a fundamental problem in quantum theory,
and information theory appears to be a useful tool.

* __Origin of correlations__:
In quantum physics there is a new kind of cause for some correlations not present
in classical physics, entanglement, which reveals itself, e.g., in correlations
that violate Bell inequalities (and hence cannot be described by common causes)
between space-like separated events (which cannot be described by classical communication);
It has been suggested that there may exist quantum correlations that go beyond entanglement,
whose existence can be revealed by quantum discord.

* __Ontological status__: Results by various
people have shown that correlations cannot be thought of as elements of reality.

@ __Reviews__: Adesso et al JPA(16)-a1605
[measures and applications].

@ __General references__: Garg & Mermin PRL(82),
FP(84) [statistical implications];
Lévy-Leblond AJP(86)feb
[generalized Heisenberg inequality for correlations];
Cabello PRA(99) [nature];
Laloë AJP(01)jun [and paradoxes];
Gisin qp/05-conf;
Higashi FP(08)
[limits to common cause approach]; Seevinck PhD(08)-a0811;
Christian FXQi-a1101 [interplay between the strength of quantum correlations and the parallelizability of manifolds]; Christian a1201 [origin of quantum correlations]; Gallego et al PRL(11) [need for multipartite information principles]; Dorner & Vedral IJMPB(13)-a1208 [historical perspective]; Cabello et al PRA(13)-a1211 [basic logical structures]; Majewski a1407-ln [quantum probability approach]; Mamone-Capria a1704 [and special relativity]; Beck a1707-BJPS [causation and information].

@ __"Correlations without correlata"__: Plotnitsky FP(03)
[Mermin's quantum mechanics]; Timpson & Brown QIP(10).

@ __And macroscopic measurements__: Navascués & Wunderlich PRS(10)-a0907 [constraints]; Ramanathan
et al PRL(11)-a1010 [local
realism].

@ __And reality, information__: Srikanth qp/01, qp/01 [information
transfer?]; Groisman et al PRA(05)qp/04 [types
of correlations, operational]; Scarani ln(11)-a0910; > s.a. quantum information.

@ __Geometry__: Pitowsky PRA(08)-a0802; Goh et al PRA(18)-a1710.

@ __Reality, ontological status__: Mermin AJP(98)sep-qp;
Cabello PRA(99)qp/98;
Seevinck FP(06)qp/05;
Walther et al PRL(06)qp/05.

@ __Related topics__: Dillenschneider
& Lutz EPL(09)-a0803 [energetics];
Allcock et al PRA(09)
[closed sets of correlations]; Cohen a1004 [between
measured and unmeasured quantities]; Williamson et al PRA(11)-a1102 [twisted]; Svetlichny a1208 [and life]; Aravinda & Srikanth IJTP-a1502 [and quantum unpredictability]; > s.a. Coherence; irreversibility in quantum theory; symmetry breaking; Work.

**Measures of Quantum Correlations** > s.a. entanglement; quantum discord.

* __Idea__: Two measures of quantum correlations are discord and entanglement.

@ __General references__: Kimura et al PRA(07)-a0705 [detecting
correlations]; Lang et al IJQI(11)-a1105 [entropic measures]; Gessner & Breuer PRL(11)-a1108 [detecting
non-classical correlations]; Yu & Zhao PRA(11)-a1307; Girolami & Adesso PRL(12)-a1110 [measure of bipartite quantum correlations]; Tufarelli et al JMP(13)-a1301 [use of the Hilbert-Schmidt metric]; Cabello et al PRL(14)-a1401 [graph-theoretic approach]; Bromley et al JPA(14)-a1404 [using the Bures distance]; de Vicente PRA(15)-a1502 [characterizing the set of quantum correlations]; Marocchi et al a1703 [distances].

@ __Geometric approach__:
Roga et al JPA(16)-a1510; Spehner et al a1611-ch [based on the Bures and Hellinger distances]; Sawicki et al a1701.

**Correlations and Non-Locality**

* __Idea__:
Measurements performed on spatially separated entangled quantum systems show correlations
that are non-local, in the sense that a Bell inequality is violated, but cannot be used
for superluminal signaling; It is also known that one can write down sets of "super-quantum''
correlations that are more non-local than is allowed by quantum mechanics,
yet are still non-signaling; > s.a. Super-Quantum Theory.

@ __General references__: Garuccio & Selleri FP(80)
[Einstein locality]; Griffiths AJP(87)jan;
Greenberger et al in(89), AJP(90)dec;
Wódkiewicz PRA(95)qp;
Mermin FP(99)qp/98;
Jordan PRA(99)
[and EPR, locality, reality]; Tommasini ht/01;
Zbinden et al PRA(01)
[and moving frames]; Barrett
et al PRA(05)qp/04 [range
of possibilities]; Brassard et al PRL(06)
[stronger correlations and communication]; Gkioulekas IJTP(08)-a0707 [breakdown over large distances]; Salart et al Nat(08)aug-a0808,
comment Kofler et al a0810 [testing
spooky action at a distance]; Skrzypczyk et al PRL(09)
[non-locality swapping]; Aolita et al PRA(12) [fully non-local correlations]; Giampaolo et al PRA(13)-a1206; Suarez a1510 [and relativistic local correlations]; Bellomo et al PRA(16)-a1601 [role of locality]; Agrawal et al IJQI(16)-a1607 [local and non-local quantumness]; > s.a. quantum locality.

@ __Proposed experiments__: Schneider a1001;
Hnilo & Agüero a1507 [timescales for stronger-than-quantum correlations].

@ __And separability / entanglement__: Home et al PLA(91)
[using non-physical probabilities]; Majewski LMP(04); Brezinski a1209; > s.a. entanglement.

**Dynamics of Correlations**

@ __General references__: Maziero et al PRA(09)-a0905 [under decoherence];
Bellomo et al PRA(12)-a1104 [and distance measures between states];
Pal & Bose EPJB(12)-a1107 [1D transverse Ising Model, classical and quantum correlations and decoherence];
Hu & Fan AP(12) [robustness against decoherence];
Bancal et al nPhys(12)-a1110 [no finite-speed causal influences];
Richerme et al Nat(14)jul-a1401 [in systems with long-range interactions];
Fröhlich & Ueltschi JMP(15)-a1412 [decay of correlations, for lattice systems in thermal equilibrium];
Ozorio de Almeida & Brodier JPA(16)-a1507 [semiclassical];
Cevolani et al a1706 [correlation spreading];
Abeling et al a1707 [buildup of spatiotemporal correlations];
> s.a. Lieb-Robinson Bounds; spin models [propagation].

@ __Thermodynamic aspects__: Oppenheim et al PRL(02);
Bruschi et al PRE(15)-a1409 [limitations and optimal protocols].

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send feedback and suggestions to bombelli at olemiss.edu – modified 22 apr 2018