Mutually Unbiased Product Bases for Multiple Qudits

Abstract

We investigate the interplay between mutual unbiasedness and product bases for multiple qudits of possibly different dimensions. A product state of such a system is shown to be mutually unbiased to a product basis only if each of its factors is mutually unbiased to all the states which occur in the corresponding factors of the product basis. This result implies both a tight limit on the number of mutually unbiased product bases which the system can support and a complete classification of mutually unbiased product bases for multiple qubits or qutrits. In addition, only maximally entangled states can be mutually unbiased to a maximal set of mutually unbiased product bases.

15 pages, identical to published version

References in corpus (3)

• Maximal Sets of Mutually Unbiased Quantum States in Dimension Six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

Cited by in corpus (10)

• Mutually unbiased bases in dimension six containing a product-vector basis
• Five open problems in quantum information
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Optimal allocation of quantum resources
• Schmidt rank constraints in Quantum Information Theory
• Constructions of mutually unbiased entangled bases
• Some special complex Hadamard matrices of order six
• The structure of product bases of ${\mathbb{C}}^2⨂{\mathbb{C}}^n$
• $H_2$-reducible matrices in six-dimensional mutually unbiased bases
• Mutually unbiased bases containing a complex Hadamard matrix of Schmidt rank three