Unextendible entangled bases with fixed Schmidt number

Unextendible maximally entangled bases and mutually unbiased bases

Unextendible Product Bases

Let C denote the complex field. A vector v in the tensor product ⊗i=1C is called a pure product vector if it is a vector of the form v1 ⊗ v2 · · · ⊗ vm, with vi ∈ Ci . A set F of pure product vectors is called an unextendible product basis if F consists of orthogonal nonzero vectors, and there is no nonzero pure product vector in ⊗i=1C which is orthogonal to all members of F . The construction ...

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...

Positive maps for bound entangled states based on unextendible product bases

In this note I show how to construct positive maps from any bound entangled state based on an unextendible product basis. These positive maps exhibit the inseparability of the corresponding bound entangled states. I illustrate the construction with an example. Typeset using REVTEX 1 It has been shown in several papers of Horodecki et al. [1–3] that there exists an intimate connection between th...

Distinguishability of complete and unextendible product bases

It is not always possible to distinguish multipartite orthogonal states if only local operation and classical communication (LOCC) are allowed. We prove that we cannot distinguish the states of an unextendible product bases (UPB) by LOCC even when infinite resources (infinite-dimensional ancillas, infinite number of operations). Moreover we give a method to check the LOCC distinguishability of ...