Purity and Gaussianity bounded uncertainty relation

Abstract

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the purity-bounded derived by V I Man'ko and V V Dodonov and the Gaussianity-bounded one [Phys. Rev. A 86, 030102R (2012)].

Major changes in the presentation of the results but also in the proofs which have become more compact. Submitted to Journal of Physics A

References in corpus (1)

• Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

Cited by in corpus (3)

• Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion
• Non-Gaussianity and entropy-bounded uncertainty relations: Application to detection of non-Gaussian entangled states
• Entropic inequalities and properties of some special functions