Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

GUSTAVO M. BOSYK; S. ZOZOR; MARIELA PORTESI; TRISTÁN M. OSÁN; PEDRO W. LAMBERTI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2014 vol. 90 p. 521141 - 521148

1050-2947

We provide a twofold extension of Landau-Pollak uncertainty relations for mixed quantum states and for positive operator-valued measures, by recourse to geometric considerations. The generalization is based on metrics between pure states, having the form of a function of the square of the inner product between the states. The triangle inequality satisfied by such metrics plays a crucial role in our derivation. The usual Landau-Pollak inequality is thus a particular case (derived from Wootters metric) of the family of inequalities obtained, and, moreover, we show that it is the most restrictive relation within the family.