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A new proof for the existence of mutually unbiased bases
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A new proof for the existence of mutually unbiased bases
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We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a constructive proof of the existence of mutually unbiased bases for dimensions which are power of a prime is presented. It is also proved that in any dimension d the number of mutually unbiased bases is at most d+1. An explicit representation of mutually unbiased observables in terms of Pauli matrices are provided for d=2^m.
Forward citations
Cited by 3 Pith papers
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Mutually Unbiased Bases for Variational Quantum Initialization: Basis-Union Optimality and Adaptive Family Search
Complete MUB ensembles are optimal for isotropic Gaussian random-Hamiltonian width among d+1 basis unions, enabling adaptive MUB-XRot QAOA that is non-worse than standard QAOA in 80% of 1500 benchmark cases.
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Mutually Unbiased Bases for Variational Quantum Initialization: Basis-Union Optimality and Adaptive Family Search
Complete MUB ensembles are optimal for isotropic Gaussian random-Hamiltonian width among d+1 basis unions, and adaptive MUB-XRot QAOA is non-worse than standard QAOA in 80% of 1500 benchmark cases across MaxCut, MIS, ...
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Efficient Gradient Estimation for Parameterized Quantum Systems with Lie Algebraic Symmetries
A gradient estimator for Lie-symmetric PQCs expresses the gradient as a linear combination of Hadamard-test expectations whose coefficients are estimated via shadow tomography, yielding logarithmic shot scaling.
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