Orthogonal product bases of four qubits

Lin Chen; Dragomir Z. Dokovic

doi:10.1088/1751-8121/aa8546

Orthogonal product bases of four qubits

Lin Chen^*
, Dragomir Z. Dokovic

^*Corresponding author for this work

School of Mathematical Sciences

University of Waterloo

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

An orthogonal product basis (OPB) of a finite-dimensional Hilbert space H = H₁ ⊗H₂⊗ ⊗ H_n is an orthonormal basis of H consisting of product vectors |x₁〉 ⊗|x₂〉 ⊗ ⊗ |x_n⊗. We show that the problem of constructing the OPBs of an n-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.

Original language	English
Article number	395301
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	50
Issue number	39
DOIs	https://doi.org/10.1088/1751-8121/aa8546
State	Published - 4 Sep 2017

Keywords

orthogonal product basis
permutation
qubit

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title = "Orthogonal product bases of four qubits",

abstract = "An orthogonal product basis (OPB) of a finite-dimensional Hilbert space H = H1 ⊗H2⊗ ⊗ Hn is an orthonormal basis of H consisting of product vectors |x1〉 ⊗|x2〉 ⊗ ⊗ |xn⊗. We show that the problem of constructing the OPBs of an n-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.",

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AU - Chen, Lin

AU - Dokovic, Dragomir Z.

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N2 - An orthogonal product basis (OPB) of a finite-dimensional Hilbert space H = H1 ⊗H2⊗ ⊗ Hn is an orthonormal basis of H consisting of product vectors |x1〉 ⊗|x2〉 ⊗ ⊗ |xn⊗. We show that the problem of constructing the OPBs of an n-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.

AB - An orthogonal product basis (OPB) of a finite-dimensional Hilbert space H = H1 ⊗H2⊗ ⊗ Hn is an orthonormal basis of H consisting of product vectors |x1〉 ⊗|x2〉 ⊗ ⊗ |xn⊗. We show that the problem of constructing the OPBs of an n-qubit system can be reduced to a purely combinatorial problem. We solve this combinatorial problem in the case of four qubits and obtain 33 multiparameter families of OPBs. Each OPB of four qubits is equivalent, under local unitary operations and qubit permutations, to an OPB belonging to at least one of these families.

KW - orthogonal product basis

KW - permutation

KW - qubit

UR - https://www.scopus.com/pages/publications/85029001814

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DO - 10.1088/1751-8121/aa8546

M3 - 文章

AN - SCOPUS:85029001814

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VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 39

M1 - 395301

ER -

Orthogonal product bases of four qubits

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Keywords

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