Improved bounds on entropic uncertainty relations

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 4, 2008, Pages

  De Vicente, Julio I ^a   Sánchez Ruiz, Jorge ^a,b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

HILBERT SPACES; SYSTEMS ANALYSIS;

INFORMATION ENTROPIES; NONCOMMUTING OBSERVABLES; UNCERTAINTY PRINCIPLE;

UNCERTAINTY ANALYSIS;

EID: 42349096443     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.042110     Document Type: Article

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33. If only PA =1/ MA, then μB = νB =0 and Eqs. 20 21 22 23 hold like in the previous cases. The analog of Eq. 16 for i=A now imposes that MA =1,2 in order to have non-negativity of the Lagrange multipliers. The solution for MA =1 gives Eq. 30, which is thus proven to be valid in principle for all values of c, while the solution for MA =2 can only hold when c≤1/2. If Pi =1/ Mi for both A and B, a similar reasoning yields Mi =1,2 for i=A,B, and the resulting bounds are clearly nonoptimal.