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| − | MSC|81P15|81P40,81R15,46L07
| + | <ref> [http://hea-www.harvard.edu/AstroStat http://hea-www.harvard.edu/AstroStat]; <nowiki> http://www.incagroup.org </nowiki>; <nowiki> http://astrostatistics.psu.edu </nowiki> </ref> |
| | | | |
| − | ===Physical origin, early theory=== | + | ====Notes==== |
| | + | <references /> |
| | + | |
| | + | ------------------------------------------- |
| | | | |
| − | ====Historic====
| |
| | | | |
| | {| | | {| |
| − | |valign="top"|{{Ref|EPR}}|| Einstein, Albert; Podolsky, Boris; Rosen, Nathan , "Can quantum-mechanical description of physical reality be considered complete?", ''Physical Review'' '''47''' (1935), 777–780. | + | | A || B || C |
| | |- | | |- |
| − | |valign="top"|{{Ref|B}}|| Bell, J. S. , "On the Einstein Podolsky Rosen paradox", ''Physics'' '''1''' (3) (1964), 195–200. | + | | X || Y || Z |
| | |} | | |} |
| | | | |
| − | ====Non-technical====
| |
| | | | |
| − | {|
| + | |
| − | |valign="top"|{{Ref|G}}|| Garg, Anupam; Mermin, N. D., "Farkas's lemma and the nature of reality: statistical implications of quantum correlations", ''Found. Phys.'' '''14''' (1984), no. 1, 1–39. {{MR|0781026}}
| + | ----------------------------------------- |
| − | |-
| + | ----------------------------------------- |
| − | |valign="top"|{{Ref|BSHC}}|| Bell, J. S.; Shimony, A.; Horne, M. A.; Clauser, J. F., "An exchange on local beables. Hidden variables and quantum uncertainty," ''Dialectica'' '''39''' (1985), no. 2, 85–110. {{MR|0806550}}
| + | |
| − | |-
| + | $\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$ |
| − | |valign="top"|{{Ref|B}}|| Bell, J. S., "Speakable and unspeakable in quantum mechanics. Collected papers on quantum philosophy", Cambridge University Press, Cambridge, 1987 {{MR|0915338}}
| + | |
| − | |-
| + | <asy> |
| − | |valign="top"|{{Ref|T}}|| Tsirelson, B. S., "Some results and problems on quantum Bell-type inequalities," ''Hadronic J. Suppl.'' '''8''' (1993), no. 4, 329–345. {{MR|1254597}}
| + | size(100,100); |
| − | |-
| + | label(scale(1.7)*'$T(\\Sigma)\hookrightarrow T(\\Sigma,X)$',(0,0)); |
| − | |valign="top"|{{Ref|WW}}|| Werner, R. F.; Wolf, M. M., "Bell's inequalities for states with positive partial transpose," ''Phys. Rev. A'' (3) '''61''' (2000), no. 6, 062102, 4 pp. {{MR|1767459}}
| + | </asy> |
| − | |-
| + | |
| − | |valign="top"|{{Ref|WW}}|| Werner, Reinhard F.; Wolf, Michael M., "Bell inequalities and entanglement," ''Quantum Inf. Comput.'' '''1''' (2001), no. 3, 1–25. {{MR|1907485}}
| + | <asy> |
| − | |-
| + | size(220,220); |
| − | |valign="top"|{{Ref|KSW}}|| Keyl, M.; Schlingemann, D.; Werner, R. F., "Infinitely entangled states," ''Quantum Inf. Comput.'' '''3''' (2003), no. 4, 281–306. {{MR|2003567}}
| + | |
| − | |-
| + | import math; |
| − | |valign="top"|{{Ref|PT}}|| Peres, Asher; Terno, Daniel R., "Quantum information and relativity theory," ''Rev. Modern Phys.'' '''76''' (2004), no. 1, 93–123. {{MR|2116831}}
| + | |
| − | |-
| + | int kmax=40; |
| − | |valign="top"|{{Ref|S}}|| Szarek, Stanislaw J., "Volume of separable states is super-doubly-exponentially small in the number of qubits," ''Phys. Rev. A'' (3) '''72''' (2005), no. 3, part A, 032304, 10 pp. {{MR|2189159}}
| + | |
| − | |-
| + | guide g; |
| − | |valign="top"|{{Ref|PWPVJ}}|| Pérez-García, D.; Wolf, M. M.; Palazuelos, C.; Villanueva, I.; Junge, M., "Unbounded violation of tripartite Bell inequalities," ''Comm. Math. Phys.'' '''279''' (2008), no. 2, 455–486. {{MR|2383595}}
| + | for (int k=-kmax; k<=kmax; ++k) { |
| − | |-
| + | real phi = 0.2*k*pi; |
| − | |valign="top"|{{Ref|JPPVW}}|| Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M., "Operator space theory: a natural framework for Bell inequalities," ''Phys. Rev. Lett.'' '''104''' (2010), no. 17, 170405, 4 pp. {{MR|2653547}}
| + | real rho = 1; |
| − | |-
| + | if (k!=0) { |
| − | |valign="top"|{{Ref|JPPVW2}}|| Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M., "Unbounded violations of bipartite Bell inequalities via operator space theory," ''Comm. Math. Phys.'' '''300''' (2010), no. 3, 715–739. {{MR|2736960}}
| + | rho = sin(phi)/phi; |
| − | |-
| + | } |
| − | |valign="top"|{{Ref|JNPPSW}}|| Junge, M.; Navascues, M.; Palazuelos, C.; Perez-Garcia, D.; Scholz, V. B.; Werner, R. F., "Connes embedding problem and Tsirelson's problem," ''J. Math. Phys.'' '''52''' (2011), no. 1, 012102, 12 pp. {{MR|2790067}}
| + | pair z=rho*expi(phi); |
| − | |-
| + | g=g..z; |
| − | |valign="top"|{{Ref|JP}}|| Junge, M.; Palazuelos, C., "Large violation of Bell inequalities with low entanglement," ''Comm. Math. Phys.'' '''306''' (2011), no. 3, 695–746. {{MR|2825506}}
| + | } |
| − | |-
| + | |
| − | |valign="top"|{{Ref|}}|| {{MR|}}
| + | draw (g); |
| − | |-
| + | |
| − | |valign="top"|{{Ref|}}|| {{MR|}}
| + | defaultpen(0.75); |
| − | |-
| + | draw ( (0,0)--(1.3,0), dotted, Arrow(SimpleHead,5) ); |
| − | |}
| + | dot ( (1,0) ); |
| | + | label ( "$a$", (1,0), NE ); |
| | + | |
| | + | </asy> |
