Southwest Quantum Information and Technology

Coherent Measuring Processes, Standard and Generalized

Presenting Author: Chris Jackson, Sandia National Laboratories
Contributing Author(s): Carlton M. Caves

The Measuring Process is a topic fundamental to Quantum Theory. Yet, the idea of measurement still isn’t understood much beyond the usual idea of single Hermitian observables, often called von Neumann measurements. Most important beyond von Neumann are the measurements associated with the laboriously named Generalized-Coherent-State (GCS) Positive Operator-Valued Measures (POVMs), a.k.a. overcomplete bases. Despite significant application to many fundamental topics such as tomography, phase space, and condensed matter theory, an understanding of the process by which the GCS POVMs can be realized is still widely underdeveloped. The overarching exception to this is the heterodyne measurement of optics, a measuring process understood mostly via the Leaky Cavity model. More recently discovered is the isotropic measuring process, a realization of the spin-coherent-state POVMs that has yet to be performed. [See link] In this talk I’ll share my understanding of Coherent Measuring Processes (CMPs)—that is, non-adaptive measuring processes which culminate into GCS POVMs—with what I call the Principle Instrument Program. How the Kraus operators of a CMP culminate into a GCS POVM is actually independent of the Hilbert space—that is, CMPs have actually nothing to do with the eigenstates of the observables being measured and thus are very different from von Neumann measurement. This departure from the Hilbert space is made by considering what I call the Kraus-operator density.

Read this article online: https://arxiv.org/abs/2107.12396, https://arxiv.org/abs/1805.01012

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