Certainty relations between local and nonlocal observables

• We point out that for an arbitrary number of identical particles, each defined on a Hilbert space of arbitrary dimension, there exists a whole ladder of relations of complementarity between certain local and nonlocal measurements corresponding to every conceivable grouping of the particles, e. g., the more accurately we can know ( by a measurement) some joint property of three qubits ( projecting the state onto a tripartite-entangled state), the less accurate some other property, local to the three qubits, becomes. We investigate the relation between these complementarity relations and a similar relation based on interference visibilities. We also show that the complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.

Keyword

mutually unbiased bases

double-slit experiment

uncertainty relations

state determination

quantum erasure

complementarity

principle

particle

wave

information

Publication and Content Type

ref (subject category)

art (subject category)