# A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

@article{Planat2004ASO, title={A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements}, author={M. Planat and H. Rosu and Serge Perrine}, journal={Foundations of Physics}, year={2004}, volume={36}, pages={1662-1680} }

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite, and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.

#### 41 Citations

Weighted complex projective 2-designs from bases : Optimal state determination by orthogonal measurements

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- 2007

Viewing sets of mutually unbiased bases as arcs in finite projective planes

- Mathematics, Physics
- 2005

Test of mutually unbiased bases for six-dimensional photonic quantum systems

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- Scientific reports
- 2013

Quantifying Measurement Incompatibility of Mutually Unbiased Bases.

- Mathematics, Medicine
- Physical review letters
- 2019

#### References

SHOWING 1-10 OF 77 REFERENCES

There is no generalization of known formulas for mutually unbiased bases

- Physics, Mathematics
- 2003

A New Proof for the Existence of Mutually Unbiased Bases

- Mathematics, Computer Science
- Algorithmica
- 2002