Optimal state-determination by mutually unbiased measurements

Lian-Fang Han, Ming Yang, Shu-Dong Fang +1 more

Bin Chen, Shao-Ming Fei

Mahdi Salehi, Seyed Javad Akhtarshenas, Mohsen Sarbishaei +1 more

A. B. Klimov, C. Muñoz, A. Fernández +1 more

We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multiqubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. H\"affner et al. [Nature (London) 438, 643 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.

Fei Yan, Ming Yang, Zhuo‐Liang Cao

Based on mutually unbiased measurements, an optimal tomographic scheme for the multiqutrit states is presented explicitly. Because the reconstruction process of states based on mutually unbiased states is free of information waste, we refer to our scheme as the optimal scheme. By optimal we mean that the number of the required conditional operations reaches the minimum in this tomographic scheme for the states of qutrit systems. Special attention will be paid to how those different mutually unbiased measurements are realized; that is, how to decompose each transformation that connects each mutually unbiased basis with the standard computational basis. It is found that all those transformations can be decomposed into several basic implementable single- and two-qutrit unitary operations. For the three-qutrit system, there exist five different mutually unbiased-bases structures with different entanglement properties, so we introduce the concept of physical complexity to minimize the number of nonlocal operations needed over the five different structures. This scheme is helpful for experimental scientists to realize the most economical reconstruction of quantum states in qutrit systems.

D�nes Petz, Katalin Mária Hangos, András Szántó +1 more

The optimal state determination (or tomography) is studied for a composite system of two qubits when measurements can be performed on one of the qubits and interactions of the two qubits can be implemented. The goal is to minimize the number of interactions to be implemented. The algebraic method used in the paper leads to an extension of the concept of mutually unbiased measurements.