Constructing unextendible product bases from multiqubit ones

Abstract

The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times 2\times 4$ and $2\times 2\times 2\times 4$ UPBs of size eight by using the existing four-qubit and five-qubit UPBs. As an application, we construct novel families of multipartite positive-partial-transpose entangled states, as well as their entanglement properties in terms of the geometric measure of entanglement.

arXiv comment30 pages

References in corpus (30)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Separability criterion and inseparable mixed states with positive partial transposition
• Quantum Nonlocality without Entanglement
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Secure key from bound entanglement
• Geometric measure of entanglement for pure multipartite states
• The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)
• Four-qubit entangled symmetric states with positive partial transpositions
• The Structure of Qubit Unextendible Product Bases
• Three-by-three bound entanglement with general unextendible product bases
• From unextendible product bases to genuinely entangled subspaces
• Bell inequalities with no quantum violation and unextendible product bases
• Strongly nonlocal unextendible product bases do exist
• Unextendible product bases and extremal density matrices with positive partial transpose
• Strong quantum nonlocality for unextendible product bases in heterogeneous systems
• Description of rank four PPT entangled states of two qutrits
• Unextendible product bases from tile structures and their local entanglement-assisted distinguishability
• Unextendible entangled bases with fixed Schmidt number
• The Minimum Size of Qubit Unextendible Product Bases
• Unextendible Product Basis for Fermionic Systems
• Separability of Completely Symmetric States in Multipartite System
• Multiqubit UPB: The method of formally orthogonal matrices
• Nonexistence of $n$-qubit unextendible product bases of size $2^n-5$
• Inertias of entanglement witnesses
• Orthogonal product bases of four qubits
• Tripartite genuinely entangled states from entanglement-breaking subspaces