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Solution to the King's problem with observables being not mutually complementary

Minoru Horibe·Akihisa Hayashi·Takaaki Hashimoto
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Abstract

We investigate the King's problem of the measurement of operators $\vec{n}_k \nobreak \cdot \nobreak \vecσ (k=1,2,3)$ instead of the three Cartesian components $σ_x$, $σ_y$ and $σ_z$ of the spin operator $\vecσ$. Here, $\vec{n}_k$ are three-dimensional real unit vectors. We show the condition over three vectors $\vec{n}_k$ to ascertain the result for measurement of any one of these operators.

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Minoru Horibe, Akihisa Hayashi, Takaaki Hashimoto. 2004-12-23. Solution to the King's problem with observables being not mutually complementary. https://doi.org/10.1103/physreva.71.032337

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