Structure of the sets of mutually unbiased bases forNqubits

2005/08/17 by J. L. Romero, G. Bjork, Gunnar Björk +3 · 4 citations
Computer Science · Engineering · Physics and Astronomy · #Coding theory and cryptography #Quantum Computing Algorithms and Architecture #graph theory and CDMA systems #quant-ph

paper · pdf · doi:10.1103/physreva.72.062310

16 pages, 10 tables, 1 figure

arxiv created 2005/08/17 · openalex publication_date 2005/12/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a system of N qubits, living in a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of 16 sets of bases, and show some of them and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.

Citations

• A Foundational Principle for Quantum Mechanics
• Discrete Wigner function and quantum-state tomography
• The mean king's problem: prime degrees of freedom
• Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
• Quantum systems with finite Hilbert space
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound

Cited by

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• The limited role of mutually unbiased product bases in dimension 6