Factor-Group-Generated Polar Spaces and (Multi-)Qudits

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group G, we first construct vector spaces over GF(p), ...

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ar X iv : 0 90 3 . 54 18 v 1 [ m at h - ph ] 3 1 M ar 2 00 9 Factor - Group - Generated Polar Spaces and ( Multi - ) Qudits

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group G, we first construct vector spaces over GF(p), ...

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ar X iv : 0 90 3 . 54 18 v 1 [ m at h - ph ] 3 1 M ar 2 00 9 Factor - Group - Generated Polar Spaces and ( Multi - ) Qudits Hans

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group G, we first construct vector spaces over GF(p), ...

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On Polar Cones and Differentiability in Reflexive Banach Spaces

Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

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Generation of qudits and entangled qudits

We propose schemes for the generation of d-level quantum states qudits and quantum entangled states of N qudits by adopting the polarization degree of freedom of photons. Arbitrary qudits can be prepared by putting d−1 identical and independent photons each with a given polarization into a single spatial and temporal mode. Then, by using N such qudits, linear optics, and proper projection measu...

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Factor-Group-Generated Polar Spaces and (Multi-)Qudits

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