Construction of mutually unbiased bases with cyclic symmetry for qubit systems

Abstract

For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well-established in theory and experiment for the past 20 years. However, most constructions of these bases make heavy use of abstract algebra and the mathematical theory of finite rings and fields, and no simple and generally accessible construction is available. This is particularly true in the case of a system composed of several qubits, which is arguably the most important case in quantum information science and quantum computation. In this paper, we close this gap by providing a simple and straightforward method for the construction of mutually unbiased bases in the case of a qubit register. We show that our construction is also accessible to experiments, since only Hadamard and controlled-phase gates are needed, which are available in most practical realizations of a quantum computer. Moreover, our scheme possesses the optimal scaling possible, i.e., the number of gates scales only linearly in the number of qubits.

4 pages, 1 figure, minor corrections

References in corpus (3)

• Experimental generation and characterization of single-photon hybrid ququarts based on polarization-orbital angular momentum encoding
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• Feynman's path integral and mutually unbiased bases

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