Unextendible Sets of Mutually Unbiased Basis Obtained from Complete Subgraphs

Unextendible mutually unbiased bases from Pauli C\classes

We provide a construction of sets of d/2 + 1 mutually unbiased bases (MUBs) in dimensions d = 4, 8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the Pauli group. What is more, specific examples of sets of MUBs obtained using our construction are shown to be strongly unextendible; that is, there does not e...

Unextendible maximally entangled bases and mutually unbiased bases

Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)

We consider questions posed in a recent paper of Mandayam et al. (2014) on the nature of “unextendible mutually unbiased bases.” We describe a conceptual framework to study these questions, using a connection proved by the author in Thas (2009) between the set of nonidentity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d a prime, and the geometry of non-degener...

Maximal Sets of Mutually Unbiased Quantum States in Dimension Six

We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the moduli of their scalar products are equal to zero, one, or 1/ √ d. These sets will be called a MU constellation, and if four MU bases were to exist for d = 6, they would give rise to 35 different MU constellations. Using a numerical minimisation procedure, we are able to identify only 1...

Separability criteria via sets of mutually unbiased measurements

Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We investigate entanglement detection using sets of MUMs and derive separability criteria for multipartite qudit systems, arbitrary high-dimensional bipartite ...