Unbiased non-orthogonal bases for tomographic reconstruction
Isabel Sainz, Luis Roa, and Andrei B. Klimov
TL;DR
This paper introduces a method to construct non-orthogonal bases with equal separations in prime dimensions, enabling optimal quantum state tomography using bi-orthogonal unbiased bases, with detailed analysis in two dimensions.
Contribution
It presents a novel general approach for creating non-orthogonal bases with equal separations and their bi-orthogonal counterparts for improved quantum tomography.
Findings
Constructed non-orthogonal bases with equal separations in prime dimensions.
Derived explicit formulas for optimal tomography using these bases.
Analyzed the special case of two-dimensional systems.
Abstract
We have developed a general method for constructing a set of non-orthogonal bases with equal separations between all different basis' states in prime dimensions.It results that the corresponding bi-orthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases we derive an explicit expression for the optimal tomography in non-orthogonal bases. Special two dimensional case is analyzed separately.
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