Abstract
We propose a method, based on the search and identification of complete subgraphs of a regular graph, to obtain sets of Pauli operators whose eigenstates form unextendible complete sets of mutually unbiased bases of n-qubit systems. With this method we can obtain results for complete and inextensible sets of mubs for 2, 3, 4 and 5 qubits.
Highlights
Mutually unbiased bases (MUBs) are of special interest because the amount of information obtained in a measurement performed in these bases about the state of a certain system contains the minimum amount of redundant information in comparison to a measurement performed on another basis
This paper is organized as follows: in Section 2, we begin with the basic definitions to introduce the problem of obtaining a WUS and complete sets of mutually unbiased bases (MUBs); in Section 3, we proceed to pose the problem formally, in terms of graphs; afterwards, in Section 4, we show the results obtained for dimensions 4, 8, 16, and 32; and in Section 5, we give a summary of our results
The complete sets of MUBs correspond to the maximal cliques K5, i.e., subgraphs with five vertices for which each one of the vertices is connected to the other four vertices of the subgraph
Summary
The generation, manipulation, and classification of the basis of n-qubits are of great importance, since those techniques have a close relationship with the reconstruction processes [1,2], together with the classification and quantification of entanglement of quantum states [3,4]. In this regard, mutually unbiased bases (MUBs) are of special interest because the amount of information obtained in a measurement performed in these bases about the state of a certain system contains the minimum amount of redundant information in comparison to a measurement performed on another basis.
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