Heisenberg uncertainty relation for three canonical observables

TY - JOUR

T1 - Heisenberg uncertainty relation for three canonical observables

AU - Kechrimparis, Spiros

AU - Weigert, Stefan

PY - 2014/12/15

Y1 - 2014/12/15

N2 - Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg uncertainty relation for the product of three standard deviations. We derive the smallest possible value of this bound and determine the specific squeezed state which saturates the triple uncertainty relation. Quantum optical experiments are proposed to verify our findings.

AB - Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg uncertainty relation for the product of three standard deviations. We derive the smallest possible value of this bound and determine the specific squeezed state which saturates the triple uncertainty relation. Quantum optical experiments are proposed to verify our findings.

UR - http://www.scopus.com/inward/record.url?scp=84918833858&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.90.062118

DO - 10.1103/PhysRevA.90.062118

M3 - Article

AN - SCOPUS:84918833858

SN - 1050-2947

VL - 90

JO - Physical Review A (Atomic, Molecular and Optical Physics)

JF - Physical Review A (Atomic, Molecular and Optical Physics)

IS - 6

M1 - 062118

ER -