All-versus-nothing (AVN) proofs [1–6] show the conflict between Einstein, Podolsky, and Rosen’s (EPR) elements of reality [7] and the perfect correlations of some quantum states. The name of “all-versus-nothing” [8] reflects a particular feature of these proofs: If one consider a set of perfect correlations and asumes EPR elements of reality, then a subset of these correlations leads to a conclusion that is opposite of the one obtained from the complementary subset of correlations.<\/p>\n
The perfect correlations among single qubit measurements required for AVN proofs are given by the 2n stabilizer operators of an n-qubit graph state. The possibility of experimentally preparing new classes of graph states [9–11] naturally leads to the following problem: Does a distribution of an n-qubit graph state between m parties allow an AVN proof? This problem has been solved for m = 2 [12]. Here we describe a method to decide whether a given n-qubit m-particle graph state allows an m-partite AVN proof specific for this state (i.e., which cannot be obtained using a graph state with fewer qubits) [13]. This method requires that two observables of each qubit are EPR elements of reality. This forces a series of constraints that are only satisfied by a reduced group of the graph state’s stabilizer operators. We detail these requirements and apply them to decide whether some n-qubit m-particle graph states recently prepared in the laboratory [9–11] allow m-partite AVN proofs.<\/p>\n
We also address the following problem: Given an n-qubit graph state, what is the minimum number m of parties that allows a specific m-partite AVN proof? The solution of this problem enables us to obtain all inequivalent distributions allowing AVN proofs with n < 9 qubits and an arbitrary number m of parties [13].<\/p>\n
These results provide the tools to help experimentalists to design tests of new AVN proofs and new Bell inequalities based on these proofs [14].<\/p>\n
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[4] A. Cabello, Phys. Rev. Lett. 86, 1911 (2001).
[5] A. Cabello, Phys. Rev. Lett. 87, 010403 (2001).
[6] A. Cabello, Phys. Rev. Lett. 95, 210401 (2005).
[7] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
[8] N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).
[9] R. Ceccarelli, G. Vallone, F. De Martini, P. Mataloni, and A. Cabello, Phys. Rev. Lett. 103, 160401 (2009).
[10] W.-B. Gao, X.-C. Yao, P. Xu, O. G\u00fchne, A. Cabello, C.-Y. Lu, C.-Z. Peng, T. Yang, Z.-B. Chen, and J.-W. Pan, arXiv:0906.3390 (2009).
[11] W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. G\u00fchne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, Nat. Phys. 6, 331 (2010).
[12] A. Cabello and P. Moreno, Phys. Rev. Lett. 99, 220402 (2007).
[13] A. Cabello and P. Moreno, Phys. Rev. A 81, 042110 (2010).
[14] A. Cabello, O. G\u00fchne, and D. Rodr\u00edguez, Phys. Rev. A 77, 062106 (2008).<\/p>\n","protected":false},"excerpt":{"rendered":"
All-versus-nothing (AVN) proofs [1–6] show the conflict between Einstein, Podolsky, and Rosen’s (EPR) elements of reality [7] and the perfect correlations of some quantum states. The name of “all-versus-nothing” [8] reflects a particular feature of these proofs: If one consider a set of perfect correlations and asumes EPR elements of reality, then a subset of […]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-902","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/902","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}