Details
| Original language | English |
|---|---|
| Journal | Quantum |
| Volume | 2 |
| Publication status | Published - 28 Mar 2018 |
Abstract
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Quantum, Vol. 2, 28.03.2018.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Additivity of entropic uncertainty relations
AU - Schwonnek, René
PY - 2018/3/28
Y1 - 2018/3/28
N2 - We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.
AB - We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.
UR - http://www.scopus.com/inward/record.url?scp=85055691408&partnerID=8YFLogxK
U2 - 10.22331/q-2018-03-30-59
DO - 10.22331/q-2018-03-30-59
M3 - Article
AN - SCOPUS:85055691408
VL - 2
JO - Quantum
JF - Quantum
SN - 2521-327X
ER -