The Limited Role of Mutually Unbiased Product Bases in Dimension Six

Abstract

We show that a complete set of seven mutually unbiased bases in dimension six, if it exists, cannot contain more than one product basis.

8 pages, identical to published version

References in corpus (4)

• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• Mutually Unbiased Bases for Continuous Variables
• Mutually Unbiased Bases and Semi-definite Programming

Cited by in corpus (18)

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• Unextendible maximally entangled bases and mutually unbiased bases
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• Mutually Unbiased Product Bases for Multiple Qudits
• Mutually unbiased bases in dimension six containing a product-vector basis
• A Note on Mutually Unbiased Unextendible Maximally Entangled Bases in ${\mathbb{C}}^2⨂{\mathbb{C}}^3$
• Mutually unbiased measurement based entanglement witnesses
• Isolated Hadamard Matrices from Mutually Unbiased Product Bases
• Small sets of complementary observables
• Unextendible Mutually Unbiased Bases from Pauli Classes
• On mutually unbiased bases: Passing from d to d**2
• Real Entries of Complex Hadamard Matrices and Mutually Unbiased Bases in Dimension Six
• Constructions of mutually unbiased entangled bases
• Comment on 'Product states and Schmidt rank of mutually unbiased bases in dimension six'
• Mutually unbiased bases containing a complex Hadamard matrix of Schmidt rank three
• Some special complex Hadamard matrices of order six
• $H_2$-reducible matrices in six-dimensional mutually unbiased bases