Coherent states with minimum Gini uncertainty for finite quantum systems

C. Lei; A. Vourdas

doi:10.1209/0295-5075/aca2d8

All issues

Volume 140 / No 4 (November 2022)

EPL, 140 4 (2022) 45001

Abstract

Issue		EPL Volume 140, Number 4, November 2022


Article Number		45001
Number of page(s)		6
Section		Atomic, molecular and optical physics
DOI		https://doi.org/10.1209/0295-5075/aca2d8
Published online		25 November 2022

EPL, 140 (2022) 45001

Coherent states with minimum Gini uncertainty for finite quantum systems

C. Lei and A. Vourdas^(a)

Department of Computer Science, University of Bradford - Bradford BD7 1DP, UK

^(a) E-mail: a.vourdas@bradford.ac.uk (corresponding author)

Received: 3 September 2022
Accepted: 14 November 2022

Abstract

Uncertainty relations $\Delta(\rho)\ge \eta_d$ in terms of the Gini index are studied. The “Gini uncertainty constant” $\eta_d$ is estimated numerically and compared to an upper bound $\tilde \eta_d\ge \eta_d$ . It is shown that for large d we get $\tilde \eta_d\approx \eta_d$ . States $|{g}\rangle$ with minimum Gini uncertainty and displacement transformations are used to define coherent states $|{\alpha, \beta}\rangle_g$ (where $\alpha, \beta \in {\mathbb Z}_d$ ) with minimum Gini uncertainty $(\Delta[|{\alpha, \beta}\rangle_g\;_g\langle{\alpha, \beta}]\approx \eta_d)$ . The $|{\alpha, \beta}\rangle_g$ resolve the identity, and therefore an arbitrary state can be expanded in terms of them. This expansion is robust in the presence of noise.

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