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 JFAP-a1704 [and special relativity]; Beck BJPS-a1707 [causation and information]; Belinsky & Shulman JRLR(17)-a1808 [possible origin].
@ "Correlations without correlata": Plotnitsky FP(03) [Mermin's quantum mechanics]; Timpson & Brown QIP(10).
@ And measurements: Navascués & Wunderlich PRS(10)-a0907 [constraints]; Ramanathan et al PRL(11)-a1010 [local realism]; Aerts & Sassoli de Bianchi a1912 [quantum correlations induced by measurements].
@ 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; Nguyen et al PRL(19)-a1808 [of EPR correlations].
@ 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; > s.a. Relationalism.
@ 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]; Jin & Fei PRA(18)-a1806 [based on the Hellinger distance]; Bhattacharyya et al a1902 [entanglement of purification].
@ Geometric approach: Roga et al JPA(16)-a1510; Spehner et al a1611-ch [based on the Bures and Hellinger distances]; Sawicki et al RPMP(18)-a1701.

Correlations and Non-Locality > s.a. causality in quantum theory [including no-signaling].
* 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]; Bussandri et al QIP(19)-a1805 [in bipartite systems]; Karlsson a1907 [local, non-classical model]; > s.a. quantum locality.
@ Proposed experiments: Schneider a1001; Hnilo & Agüero a1507 [time scales 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 > s.a. open quantum systems.
@ 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 PRB(18)-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]; > s.a. generalized thermodynamics.

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