# MUBs: From Finite Projective Geometry to Quantum Phase Enciphering

@article{Rosu2004MUBsFF, title={MUBs: From Finite Projective Geometry to Quantum Phase Enciphering}, author={H. Rosu and M. Planat and M. Saniga}, journal={arXiv: Quantum Physics}, year={2004}, volume={734}, pages={315-318} }

This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension.

#### 6 Citations

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

- Mathematics, Physics
- 2004

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… Expand

Quantum Primitives

- 2009

We explore possible characterisations of entanglement classes which may be interpreted as gates acting on globally distributed systems. The cyclic nature of a selection of entanglement gates,… Expand

A classification of finite quantum kinematics

- Mathematics, Physics
- 2014

Quantum mechanics in Hilbert spaces of finite dimension $N$ is reviewed from the number theoretic point of view. For composite numbers $N$ possible quantum kinematics are classified on the basis of… Expand

Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

- Mathematics, Physics
- 2008

The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger (GHZ) basis are studied. These are a natural generalization of… Expand

Mutually orthogonal Latin squares from the inner products of vectors in mutually unbiased bases

- Mathematics
- 2010

Mutually unbiased bases (MUBs) are important in quantum information theory. While constructions of complete sets of d + 1 MUBs in C-d are known when d is a prime power, it is unknown if such complete… Expand

A Quantum Stochastic Calculus

- Mathematics
- 2012

Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers… Expand

#### References

SHOWING 1-5 OF 5 REFERENCES

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

- Mathematics, Physics
- 2004

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… Expand

Projective geometry - from foundations to applications

- Mathematics, Computer Science
- 1998

1. Synthetic geometry 2. Analytic geometry 3. The representation theorems 4. Quadratic sets 5. Applications of geometry to coding theory 6. Applications of geometry in cryptography.

On SIC-POVMs and MUBs in Dimension 6

- Physics, Mathematics
- 2004

We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions.
An algebraic… Expand

Quantendesigns”, Dissertation in German, Wien

- 1999