Southwest Quantum Information and Technology

Implementation and applications of generalized coherent-state measurement: Case study: SU(2) and SU(1,1)

Presenting Author: Ezad Shojaee, University of New Mexico CQuIC
Contributing Author(s): Christopher S. Jackson Carlos A. Riofrio Amir Kalev Ivan H. Deutsch

Generalized coherent-states (GCS) are obtained by applying the unitary representations of elements of a Lie group onto a chosen fiducial state in Hilbert space. These states form an over-complete basis set which resolves the identity and form a positive-operator-valued-measure (POVM). The measurement with POVM elements proportional to GCSs is called the coherent-state measurement. In this work, we show how any such POVM can be obtained through a sequence of weak measurements of a fiducial operator, conjugated by Haar-random elements of the group. We study two important groups: SU(2) and SU(1,1). The SU(2) coherent-state measurement is a way to optimally estimate the state of an unknown pure qubit given a finite number of copies and can be implemented by doing a sequence of collective isotropic weak measurements of the collective spin projection. SU(1,1) coherent-state measurement forms a POVM over the set of squeezed-vacuum states. This measurement can be implemented by weakly measuring the number operator isotropically conjugated with squeezers. We consider its applications in metrology.

Read this article online: 10.1103/PhysRevLett.121.130404

(Session 5 : Sunday from 5:00pm - 7:00pm)