11 research outputs found
Entropy and the uncertainty principle
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about
classical entropies associated to quantum density matrices. These theorems
refer to the classical entropies of the diagonals of a density matrix in two
different bases. Thus they provide a kind of uncertainty principle. Our
inequalities are sharp because they are exact in the high-temperature or
semi-classical limit.Comment: 6 page
Extended quantum conditional entropy and quantum uncertainty inequalities
Quantum states can be subjected to classical measurements, whose
incompatibility, or uncertainty, can be quantified by a comparison of certain
entropies. There is a long history of such entropy inequalities between
position and momentum. Recently these inequalities have been generalized to the
tensor product of several Hilbert spaces and we show here how their derivations
can be shortened to a few lines and how they can be generalized. All the
recently derived uncertainty relations utilize the strong subadditivity (SSA)
theorem; our contribution relies on directly utilizing the proof technique of
the original derivation of SSA.Comment: 4 page
Inequalities on time-concentrated or frequency-concentrated functions
10.1007/s10444-004-4145-xAdvances in Computational Mathematics241-4333-35