Unextendible Maximally Entangled Bases in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$

Abstract

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in ${\mathbb{C}}^{pd}\otimes {\mathbb{C}}^{qd}$($p\le q$) based on the constructions of UMEBs in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ and in ${\mathbb{C}}^p\otimes {\mathbb{C}}^q$, which generalizes the results in [Phys. Rev. A. 94, 052302 (2016)] by two approaches. Two different 48-member UMEBs in ${\mathbb{C}}^6\otimes {\mathbb{C}}^9$ have been constructed in detail.

References in corpus (14)

• Quantum entanglement
• Unextendible Product Bases and Bound Entanglement
• Quantum Cryptography using entangled photons in energy-time Bell states
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Distinguishability of complete and unextendible product bases
• 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
• Multipartite unextendible entangled basis
• Unextendible entangled bases with fixed Schmidt number
• Entangled bases with fixed Schmidt number
• Constructing UMEB from maximally entangled basis
• Unextendible maximally entangled bases and mutually unbiased bases in multipartite systems
• Connecting the UMEB in ${\mathbb{C}}^d⨂{\mathbb{C}}^d$ with partial Hadamard matrices

Cited by in corpus (5)

• Multipartite unextendible entangled basis
• Separability and entanglement in superpositions of quantum states
• Unextendible entangled bases and more nonlocality with less entanglement
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
• An extension of Bravyi-Smolin's construction for UMEBs