Tilted phase space measurements

Abstract

We show that the phase shift of π/2 is crucial for the phase space translation covariance of the measured high-amplitude limit observable in eight-port homodyne detection. However, for an arbitrary phase shift θ we construct explicitly a different nonequivalent projective representation of R${}^2$ such that the observable is covariant with respect to this representation. As a result we are able to determine the measured observable for an arbitrary parameter field and phase shift. Geometrically the change in the phase shift corresponds to the tilting of one axis in the phase space of the system.

4 pages, 4 figures

References in corpus (4)

• Positive operator valued measures covariant with respect to an irreducible representation
• On the coexistence of position and momentum observables
• A note on the measurement of phase space observables with an eight-port homodyne detector
• Inefficient eight-port homodyne detection and covariant phase space observables