Details
| Original language | English |
|---|---|
| Article number | 1550045 |
| Pages (from-to) | 1550045 |
| Number of pages | 1 |
| Journal | Int. J. Quant. Inf. |
| Volume | 13 |
| Issue number | 6 |
| Publication status | Published - 1 Sept 2015 |
Abstract
The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be nonoptimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work, we establish optimal uncertainty relations by characterizing the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalize various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.
Keywords
- Entropy, optimality, uncertainty relations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Int. J. Quant. Inf., Vol. 13, No. 6, 1550045, 01.09.2015, p. 1550045.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Optimality of entropic uncertainty relations
AU - Abdelkhalek, Kais
AU - Schwonnek, René
AU - Maassen, Hans
AU - Furrer, Fabian
AU - Duhme, Jörg
AU - Raynal, Philippe
AU - Englert, Berthold-Georg
AU - Werner, Reinhard F.
N1 - Funding information: The work in Singapore is funded by the Singapore Ministry of Education (partly through the Academic Research Fund Tier 3 MOE2012-T3-1-009) and the National Research Foundation of Singapore. F.F. acknowledges support from LUH GRK 1463 and the Japan Society for the Promotion of Science (JSPS) by KAKENHI Grant No. 24-02793. R.S. acknowledges support from the BMBF funded network Q.com-Q.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be nonoptimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work, we establish optimal uncertainty relations by characterizing the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalize various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.
AB - The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be nonoptimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work, we establish optimal uncertainty relations by characterizing the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalize various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.
KW - Entropy
KW - optimality
KW - uncertainty relations
UR - http://www.scopus.com/inward/record.url?scp=84948720630&partnerID=8YFLogxK
U2 - 10.1142/S0219749915500458
DO - 10.1142/S0219749915500458
M3 - Article
VL - 13
SP - 1550045
JO - Int. J. Quant. Inf.
JF - Int. J. Quant. Inf.
IS - 6
M1 - 1550045
ER -