publication . Preprint . Article . 2011

Probabilistic Generation of Quantum Contextual Sets

Norman D. Megill; Krešimir Fresl; Mordecai Waegell; P.K. Aravind; Mladen Pavičić;
Open Access English
  • Published: 09 May 2011
We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. Using a random sample of the sets generated with our method, we give a statistical estimate of the number of sets that might be obtained in an eventual exhaustive enumeration.
free text keywords: Quantum Physics, General Physics and Astronomy, Quantum, Discrete mathematics, Physics, Quantum mechanics, Quantum gate, Parity (mathematics), Hypergraph, Constraint graph, Probabilistic logic, Enumeration, 600-cell
Funded by
MZOS| Quantum Computation: Parallelism and Visualization
  • Funder: Ministry of Science, Education and Sports of the Republic of Croatia (MSES) (MZOS)
  • Project Code: 082-0982562-3160
30 references, page 1 of 2

[1] M.Hein, J. Eisert, H. J. Briegel, Multiparty entanglement in graph states, Phys. Rev. A 69 (2004) 062311-1-20.

[2] A. Cabello, P. Moreno, All-versus-nothing proofs with n qubits distributed between m parties, Phys. Rev. A 81 (2010) 042110, ArXiv:1004.4874v1.

[3] A. Cabello, Proposal for revealing quantum nonlocality via local contextuality, Phys. Rev. Lett. 104 (2010) 2210401-1-4, ArXiv:0910.5507v4.

[4] M. Paviˇci´c, B. D. McKay, N. D. Megill, K. Fresl, Graph approach to quantum systems, J. Math. Phys. 51 (2010) 102103-1-31.

[5] N. D. Megill, M. Paviˇci´c, Kochen-Specker sets and generalized Orthoarguesian equations, Ann. Henri Poincar´e 11, ArXiv:abs/1005.0016.

[6] M. Paviˇci´c, Exhaustive generation of orthomodular lattices with exactly one non-quantum state, Rep. Math. Phys. 64 (2009) 417-428.

[7] C. Simon, H. Weinfurter, M. Z˙ukowski, A. Zeilinger, Feasible KochenSpecker experiment with single particles, Phys. Rev. Lett. 85 (2000) 1783- 1786.

[8] M. Michler, H. Weinfurter, M. Z˙ ukowski, Experiments towards falsification of noncontextual hidden variables, Phys. Rev. Lett. 84 (2000) 5457-5461, ArXiv:quant-ph/0009061. [OpenAIRE]

[9] A. Cabello, “All versus nothing” inseparability for two observers, Phys. Rev. Lett 75 (2001) 010403-1-4, ArXiv:quant-ph/0101108v5.

[10] Y.-F. Huang, C.-F. Li, J.-W. P. Yong-Sheng Zhang, G.-C. Guo, Experimental test of the Kochen-Specker theorem with single photons, Phys. Rev. Lett. 90 (2003) 250401-1-4.

[11] Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, H. Rauch, Quantum contextuality in a single-neutron optical experiment, Phys. Rev. Lett. 97 (2006) 230401-1-4. [OpenAIRE]

[12] A. Cabello, S. Filipp, H. Rauch, Y. Hasegawa, Proposed experiment for testing quantum contextuality with neutrons, Phys. Rev. Lett. 100 (2008) 130404-1-4.

[13] H. Bartosik, J. Klep, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Experimental test of quantum contextuality in neutron interferometry, Phys. Rev. Lett. 103 (2009) 040403-1-4. [OpenAIRE]

[14] G. Kirchmair, F. Za¨hringer, R. Gerritsma, M. Kleinmann, O. Gu¨hne, A. Cabello, R. Blatt, C. F. Roos, State-independent experimental test of quantum contextuality, Nature 460 (2009) 494-497, ArXiv:0904.1655v2.

[15] E. Amselem, M. R˚admark, M. Bourennane, A. Cabello, State-independent quantum contextuality with single photons, Phys. Rev. Lett. 103 (2009) 160405-1-4, ArXiv:0907.4494v2. [OpenAIRE]

30 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Article . 2011

Probabilistic Generation of Quantum Contextual Sets

Norman D. Megill; Krešimir Fresl; Mordecai Waegell; P.K. Aravind; Mladen Pavičić;