Kochen-Specker Algorithms for Qunits

Algorithms for finding arbitrary sets of Kochen-Specker (KS) qunits (n-level systems) as well as all the remaining vectors in a space of an arbitrary dimension are presented. The algorithms are based on linear MMP diagrams which generate orthogonalities of KS qunits, on an algebraic definition of states on the diagrams, and on nonlinear equations corresponding to MMP diagrams whose solutions are either KS qunits or the remaining vectors of a chosen space depending on whether the diagrams allow 0-1 states or not. The complexity of the algorithms is polynomial. New results obtained with the help of the algorithms are presented.Comment: 4 pages, 4 figures, appeared in Barnett, S.M., Andersson, E., Jeffers, J., Ohberg, P., and Hirota, O., (Eds), QCMC 2004. Quantum Communication, Measurement and Computing: The Seventh International Conference on Quantum Communication, Measurement and Computing held in Glasgow, United Kingdom, 25-29 July 2004, American Institute of Physics Conference Proceedings 734, 2004, pp. 195-198, under the title "Kochen-Specker algorithms for qubits"; qubits changed into qunits here; 3 typos corrected; Web page: http://m3k.grad.hr/pavici

Spin-correlated interferometry with beam splitters: preselection of spin-correlated photons

A nonclassical feature of the fourth-order interference at a beam splitter, that genuine photon spin singlets are emitted in predetermined directions even when incident photons are unpolarized, has been used in a proposal for an experiment that imposes quantum spin correlation on truly independent photons. In the experiment, two photons from two such singlets interfere at a beam splitter, and as a result the other two photons - which nowhere interacted and whose paths nowhere crossed - exhibit a 100% correlation in polarization, even when no polarization has been measured in the first two photons. The propsed experiment permits closure of the remaining loopholes in the Bell theorem proof and reveals the quantum nonlocality as a property of selection, and pioneers an experimental procedure for exact preparation of unequal superposition.Comment: RevTeX, 19 pages, 3 ps figures, author's www: http://m3k.grad.hr/pavici