Multipartite unextendible entangled basis

Abstract

The unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) in ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}$ is proposed in [Phys. Rev. A 90 (2014) 054303], $1<k\le \min \{d_1,d_2\}$, which is a set of orthonormal entangled states with Schmidt number $k$ in a $d_1\otimes d_2$ system consisting of fewer than $d_1{d}_2$ vectors which have no additional entangled vectors with Schmidt number $k$ in the complementary space. In this paper, we extend it to multipartite case and a general way of constructing $(m+1)$-partite UEBk from $m$-partite UEBk is proposed ($m\ge 2$). Consequently, we show that there are infinitely many UEBks in ${\mathbb{C}}^{d_1}\otimes {\mathbb{C}}^{d_2}\otimes \cdots \otimes {\mathbb{C}}^{d_N}$ with any dimensions and any $N\ge 3$.

16 pages. Some minors are corrected

References in corpus (8)

• Entanglement detection
• Unextendible maximally entangled bases and mutually unbiased bases
• Unextendible maximally entangled bases in ${\mathbb{C}}^d⨂{\mathbb{C}}^{d^{\prime }}$
• Unextendible maximally entangled bases in dxd
• Entangled bases with fixed Schmidt number
• Unextendible entangled bases with fixed Schmidt number
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$
• Unextendible Maximally Entangled Bases in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$

Cited by in corpus (13)

• Superactivation of monogamy relations for nonadditive quantum correlation measures
• Any entanglement of assistance is polygamous
• Constructing UMEB from maximally entangled basis
• Unextendible Maximally Entangled Bases in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$
• Separability and entanglement in superpositions of quantum states
• Unextendible maximally entangled bases and mutually unbiased bases in multipartite systems
• Unextendible entangled bases and more nonlocality with less entanglement
• Constructions of Unextendible Maximally Entangled Bases in \(\mathbb {C}^{d}\otimes \mathbb {C}^{d^{\prime}}\)
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• Polygamy relation of quantum correlations with equality
• Strong nonlocal sets of UPB
• Special unextendible entangled bases with continuous integer cardinality
• Constructions of unextendible entangled bases