Unextendible maximally entangled bases in $${\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}$$ C pd ⊗ C qd

Unextendible maximally entangled bases and mutually unbiased bases

Frames for subspaces of $\mathbb{C}^N$

We present a theory of finite frames for subspaces of C N. The definition of a subspace frame is given and results analogous to those from frame theory for C N are proven.

Locally unextendible non-maximally entangled basis

We introduce the concept of the locally unextendible non-maximally entangled basis (LUNMEB) in H ⊗ H. It is shown that such a basis consists of d orthogonal vectors for a non-maximally entangled state. However, there can be a maximum of (d − 1) orthogonal vectors for non-maximally entangled state if it is maximally entangled in (d− 1) dimensional subspace. Such a basis plays an important role i...

mathbb { Z } ) } $ $ have the stacked bases property ?

It is known that a Prüfer domain either with dimension 1 or with finite character has the stacked bases property. Following Brewer and Klinger, some rings of integer-valued polynomials provide, for every n ≥ 2, examples of n-dimensional Prüfer domains without finite character which have the stacked bases property. But, the following question is still open: does the two-dimensional Prüfer domain...

Computing minimal interpolants in $C^{1, 1}(\mathbb{R}^d)$

We consider the following interpolation problem. Suppose one is given a finite set E ⊂ R, a function f : E → R, and possibly the gradients of f at the points of E. We want to interpolate the given information with a function F ∈ C(R) with the minimum possible value of Lip(∇F ). We present practical, efficient algorithms for constructing an F such that Lip(∇F ) is minimal, or for less computatio...