Bell inequalities play a central rôle in the study of quantum non-locality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality whic...

The Bell number B, is the number of partitions of a finite set whose cardinality is n. The modular properties of Bell numbers have been studied by many authors. It is well known that the sequence of the residues of Bell numbers modulo any integer satisfies a linear recurrence and is periodic [ 1, 68, 13, 143. When the modulus is prime, this recurrence is particularly simple. Touchard [16] shows...

A new decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic inequality of the coefficients of a given Bell diagonal states and can be derived via a simple algorithmic calculation of its invariants. In addition, the criterion can be extended to a quantum system of higher dimension. Keyw...

All lectures will be held in Max Bell 159 (Max Bell Building accessible by walkway on 2nd floor of Corbett Hall). LCD projector, overhead projectors and blackboards are available for presentations. Please note that the meeting space designated for BIRS is the lower level of Max Bell, Rooms 155–159. Please respect that all other space has been contracted to other Banff Centre guests, including a...

In Bell experiments, one problem is to achieve high enough photodetection to ensure that there is no possibility of describing the results via a local hidden-variable model. Using the Clauser-Horne inequality and a two-photon nonmaximally entangled state, a photodetection efficiency higher than 0.67 is necessary. Here we discuss atom-photon Bell experiments. We show that, assuming perfect detec...

The 2-adic valuations of Bell and complementary Bell numbers is determined. The complementary Bell numbers are known to be zero at n = 2 and H. S. Wilf conjectured that this is the only case where vanishing occurs. N. C. Alexander and J. An prove (independently) that there are at most two indices where this happens. This paper presents yet an alternative proof of the latter.