TY - JOUR

T1 - Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum

AU - Kechrimparis, Spyridon

AU - Weigert, Stefan Ludwig Otto

N1 - © 2017 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2017/12/11

Y1 - 2017/12/11

N2 - For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by N linear combinations of position and momentum observables. The bounds depend on their degree of incompatibility defined by the area of a parallelogram in an N-dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position andmomentum Shannon entropies of the particle.

AB - For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by N linear combinations of position and momentum observables. The bounds depend on their degree of incompatibility defined by the area of a parallelogram in an N-dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position andmomentum Shannon entropies of the particle.

U2 - 10.1088/1751-8121/aa9cfc

DO - 10.1088/1751-8121/aa9cfc

M3 - Article

SN - 1751-8113

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 2

M1 - 025303

ER -