Mutually Unbiased Quantum Observables

• URL: http://arxiv.org/abs/2110.03099v1
• Date: Wed, 6 Oct 2021 23:07:41 GMT
• Title: Mutually Unbiased Quantum Observables
• Authors: Stan Gudder
• Abstract summary: We define mutually unbiased (MU) observables on a finite dimensional Hilbert space. Relationships between MU observables, value-complementary observables and two other conditions involving sequential products of observables are discussed. finite position and momentum observables are employed to give examples of parts of MU observables that are value-complementary and those that are not.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables and two other conditions involving sequential products of observables are discussed. We next present a special motivating case of MU observables called finite position and momentum observables. These are atomic observables related by a finite Fourier transform. Finite position and momentum observables are employed to give examples of parts of MU observables that are value-complementary and those that are not value-complementary. Various open problems involving these concepts are presented. These problems mainly involve extending this work from sharp observables to unsharp observables.

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