Mutually Unbiased Bases and Complementary Spin 1 Observables - Quantum PhysicsReport as inadecuate

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Abstract: The two observables are complementary if they cannot be measuredsimultaneously, however they become maximally complementary if theireigenstates are mutually unbiased. Only then the measurement of one observablegives no information about the other observable. The spin projection operatorsonto three mutually orthogonal directions are maximally complementary only forthe spin 1-2. For the higher spin numbers they are no longer unbiased. In thiswork we examine the properties of spin 1 Mutually Unbiased Bases MUBs andlook for the physical meaning of the corresponding operators. We show that ifthe computational basis is chosen to be the eigenbasis of the spin projectionoperator onto some direction z, the states of the other MUBs have to besqueezed. Then, we introduce the analogs of momentum and position operators andinterpret what information about the spin vector the observer gains whilemeasuring them. Finally, we study the generation and the measurement of MUBsstates by introducing the Fourier like transform through spin squeezing. Thehigher spin numbers are also considered.

Author: Pawel Kurzynski, Wawrzyniec Kaszub, Mikolaj Czechlewski



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