# ON MUTUALLY UNBIASED BASES

@article{Durt2010ONMU, title={ON MUTUALLY UNBIASED BASES}, author={Thomas Durt and Berthold-Georg Englert and Ingemar Bengtsson and Karol Życzkowski}, journal={International Journal of Quantum Information}, year={2010}, volume={08}, pages={535-640} }

Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of important questions that have not been answered in full as yet. In particular, one can find maximal sets of N + 1 mutually unbiased bases in Hilbert spaces of prime-power dimension N = pM, with p prime and M a positive integer, and there is a continuum of…

## 345 Citations

Entanglement in mutually unbiased bases

- Physics
- 2011

One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to…

Quantifying Measurement Incompatibility of Mutually Unbiased Bases.

- Computer SciencePhysical review letters
- 2019

This work quantifies precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness using the standard construction for d being a prime power, and provides upper and lower bounds on this quantity for sets of k MUB in dimension d.

Weak mutually unbiased bases

- Mathematics
- 2012

Quantum systems with variables in are considered. The properties of lines in the phase space of these systems are studied. Weak mutually unbiased bases in these systems are defined as bases for which…

Mutually Unbiased Quantum Bases : Existence , Entanglement , Information

- Computer Science
- 2015

The difficulties of those approaches to the existence problem which employ Hadamard matrices are explored and new general results are derived for the connection between MUBs and Unitary Operator Bases and the role of entanglement is explored.

Graph-state formalism for mutually unbiased bases

- Computer Science
- 2013

A novel method based on the graph-state formalism to construct complete sets of mutually unbiased bases (MUBs) for n-level systems, and it is shown that a single $n$-dimensional vector can be used to generate a complete set of MUBs.

Partial ordering of weak mutually unbiased bases

- Mathematics
- 2014

A quantum system with variables in , where (with prime numbers), is considered. The non-near-linear geometry of the phase space , is studied. The lines through the origin are factorized in terms of…

Orthogonal Pairs and Mutually Unbiased Bases

- Mathematics
- 2015

The goal of our article is a study of related mathematical and physical objects: orthogonal pairs in sl(n) and mutually unbiased bases in ℂn. An orthogonal pair in a simple Lie algebra is a pair of…

Entanglement patterns in mutually unbiased basis sets

- Physics
- 2011

A few simply stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs) and constrain the combinations of such patterns that can coexist in full complements…

Tomographically complete sets of orthonormal bases in finite systems

- Mathematics
- 2011

Quantum systems where the position and momentum are in the ring (d is an odd integer) are considered. A tomographically complete set of bases, i.e. a set of bases such that probabilities from…

Constructing Extremal Compatible Quantum Observables by Means of Two Mutually Unbiased Bases

- MathematicsFoundations of Physics
- 2019

We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as…

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