Fundamental Limitations for Measurements in Quantum Many-Body Systems

Journal Article (Journal Article)

Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently if we have access to a certain set of experimentally realizable measurements and can extend it through time evolution. For the latter, two scenarios are considered: (a) evolution according to unitary circuits and (b) evolution due to Hamiltonians that we can control in a time-dependent fashion. We find that the time needed to realize a certain measurement to a predefined accuracy scales in general exponentially with the system size - posing a fundamental limitation. The argument is based on the construction of μ-packings for manifolds of observables with identical spectra and a comparison of their cardinalities to those of μ-coverings for quantum circuits and unitary time-evolution operators. The former is related to the study of Grassmann manifolds.

Full Text

Duke Authors

Cited Authors

  • Barthel, T; Lu, J

Published Date

  • August 24, 2018

Published In

Volume / Issue

  • 121 / 8

PubMed ID

  • 30192598

Electronic International Standard Serial Number (EISSN)

  • 1079-7114

International Standard Serial Number (ISSN)

  • 0031-9007

Digital Object Identifier (DOI)

  • 10.1103/PhysRevLett.121.080406

Citation Source

  • Scopus