Abstract
In Hall’s reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the uncertainty relation, we present new bounds for the information exclusion relation using majorization theory and combinatoric techniques, which reveal further characteristic properties of the overlap matrix between the measurements.
Highlights
In Hall’s reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle
The sum of information corresponding to measurements of position and momentum is bounded by the quantity log2ΔXΔPX/ħ; for a quantum system with uncertainties for complementary observables ΔX and ΔPX, and this is equivalent to one form of the Heisenberg uncertainty principle10
For observables M1, M2, ..., MN, where r(M1, M2, ..., MN, B) is a nontrivial quantum bound. Such a quantum bound is recently given by Zhang et al.18 for the information exclusion principle of multi-measurements in the presence of the quantum memory
Summary
In Hall’s reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. The sum of information corresponding to measurements of position and momentum is bounded by the quantity log2ΔXΔPX/ħ; for a quantum system with uncertainties for complementary observables ΔX and ΔPX, and this is equivalent to one form of the Heisenberg uncertainty principle. The sum of information corresponding to measurements of position and momentum is bounded by the quantity log2ΔXΔPX/ħ; for a quantum system with uncertainties for complementary observables ΔX and ΔPX, and this is equivalent to one form of the Heisenberg uncertainty principle10 Both the uncertainty relation and information exclusion relation have been used to study the complementarity of obervables such as position and momentum. For observables M1, M2, ..., MN, where r(M1, M2, ..., MN, B) is a nontrivial quantum bound Such a quantum bound is recently given by Zhang et al. for the information exclusion principle of multi-measurements in the presence of the quantum memory. Almost all available bounds are not tight even for the case of two observables
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
