Exact uncertainty relations: technical details

Details Exact uncertainty relations: technical details Exact uncertainty relations: technical details

2001-03-14

arxiv.org/abs/quant-ph/0103072v3

Physics

Quantum Physics

Latex, minor corrections/clarifications. A related, substantially shorter paper focusing on phsyical significance is at quant-

Scientific paper

The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact" uncertainty relation is discussed, and results are generalised to angular momentum and phase, photon number and phase, time and frequency, and to states described by density operators. Connections to optimal estimation of an observable from the measurement of a second observable, Wigner functions, energy bounds, and entanglement are also given.

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