# Multiqubit UPB: the method of formally orthogonal matrices

@article{Chen2018MultiqubitUT,
title={Multiqubit UPB: the method of formally orthogonal matrices},
author={Lin Chen and Dragomir Ž. Đokovi{\'c}},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2018},
volume={51}
}
• Published 26 January 2018
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
We use formal matrices whose entries we view as vector variables taking unit vector values in one-qubit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and provide a new construction of UPBs of n qubits of cardinality n  +  1 when . We also give a new method of constructing multiqubit entangled states with all partial transposes positive.
9 Citations

### Constructing unextendible product bases from multiqubit ones

• Physics
Communications in Theoretical Physics
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The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of 2 × 2 × 4 and 2 × 2 × 2 × 4 UPBs of size

### The construction of 7-qubit unextendible product bases of size ten

• Physics
Quantum Inf. Process.
• 2020
The construction of multiqubit unextendible product bases (UPBs) is an important problem in quantum information and the results solve an open problem proposed in (J Phys A 51:265302, 2018).

### The construction and local distinguishability of multiqubit unextendible product bases

• Mathematics
• 2021
An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs). By using the unextendible orthogonal matrices, we construct a 7-qubit UPB of size 11. It

### The unextendible product bases of four qubits: Hasse diagrams

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Quantum Inf. Process.
• 2019
This work considers the unextendible product bases (UPBs) of fixed cardinality m in quantum systems of n qubits, and uses this partial order to study the topological closure of an equivalence class of UPBs.

### Constructing 2 × 2 × 4 and 4 × 4 unextendible product bases and positive-partial-transpose entangled states

• Physics
Linear and Multilinear Algebra
• 2019
The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and

### $4\times4$ unextendible product basis and genuinely entangled space

• Physics
• 2019
We show that there are six inequivalent $4\times4$ unextendible product bases (UPBs) of size eight, when we consider only 4-qubit product vectors. We apply our results to construct

### $$4\times 4$$4×4 unextendible product basis and genuinely entangled space

• Mathematics
Quantum Inf. Process.
• 2019
It is shown that there are six inequivalent unextendible product bases (UPBs) of size eight, when the authors consider only 4-qubit product vectors, and one of the six UPBs turns out to be orthogonal to an incompletely genuinely entangled space.

### Constructing $2\times2\times4$ and $4\times4$ unextendible product bases and positive-partial-transpose entangled states

• Physics
• 2018
The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and

### Construction of multipartite unextendible product bases and geometric measure of entanglement of positive-partial-transpose entangled states

• Yize SunBaoshan WangShiru Li
• Physics
• 2022
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space C⊗C⊗C⊗ C⊗C⊗C by

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