# Uncertainty relations based on mutually unbiased measurements

Uncertainty relations based on mutually unbiased measurements We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $$d+1$$ d + 1 MUMs on any density operator $$\rho$$ ρ in $${\mathbb {C}}^{d}$$ C d , both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Uncertainty relations based on mutually unbiased measurements

, Volume 14 (6) – Feb 20, 2015
12 pages

/lp/springer_journal/uncertainty-relations-based-on-mutually-unbiased-measurements-IKP2dQE1dG
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0949-5
Publisher site
See Article on Publisher Site

### Abstract

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $$d+1$$ d + 1 MUMs on any density operator $$\rho$$ ρ in $${\mathbb {C}}^{d}$$ C d , both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 20, 2015

### References

• The uncertainty principle
Robertson, HP

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