Mutually disjoint, maximally commuting set of physical observables for optimum state determination

We consider the state determination problem using mutually unbiased bases (MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli operators of spin-1/2 system, which are experimentally implementable and correspond to the optimum measurement in characterizing the density matrix, we descri...

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Bibliographic Details
Published inPhysica scripta Vol. 94; no. 10; pp. 105212 - 105218
Main Authors Smitha Rao, H S, Sirsi, Swarnamala, Bharath, Karthik
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.10.2019
Subjects
complete set of commuting operators
mutually unbiased bases (MUBs)
optimal measurement
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Summary:We consider the state determination problem using mutually unbiased bases (MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli operators of spin-1/2 system, which are experimentally implementable and correspond to the optimum measurement in characterizing the density matrix, we describe a procedure to construct an orthonormal set of operators from MUBs. The constructed operators are maximally commuting, can be physically realized, and correspond to physical observables. The method of construction is general enough to allow for extensions to higher-dimensional spin systems and arbitrary density matrices in finite dimensions for which MUBs are known to exist.
Bibliography:PHYSSCR-108640.R1
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/ab2a85