2009/05/11 by Paweł Kurzyński, Pawel Kurzynski, Wawrzyniec Kaszub +2
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Chemistry #Eigenvalues and eigenvectors #Hilbert space #Mathematics #Mutually unbiased bases #Observable #Observer (physics) #Operator (biology) #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Spin (aerodynamics) #Theoretical physics #quant-ph
paper · pdf · doi:10.1088/1751-8113/43/26/265303
published as J. Phys. A: Math. Teor. J. 43, 265303 (2010) · 7 pages, 3 figures, comments welcome
arxiv created 2009/05/11 · openalex publication_date 2010/06/04 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The two observables are incompatible if they cannot be measured simultaneously; however, they become maximally incompatible (complementary) if their eigenstates are mutually unbiased. Only then does the measurement of one observable give no information about the other observable. The spin projection operators onto three mutually orthogonal directions are complementary only for spin 1/2. For higher spin numbers the corresponding eigenstates are no longer unbiased. In this work we examine the properties of spin 1 mutually unbiased bases (MUB) and look for the physical meaning of the corresponding operators. We show that if the computational basis is chosen to be the eigenbasis of the spin projection operator along some direction z , then all the states, which are unbiased to this basis, have to be squeezed. Next, we study the generation and the measurement of MUB states by introducing the Fourier-like transform through spin squeezing. Finally, we try to ascribe some classical interpretation to the operators corresponding to MUB and study what information the observer gains while measuring them. Higher spin numbers are also considered.