Communications in Mathematical Physics

, Volume 331, Issue 2, pp 431–475

A Generalization of Schur–Weyl Duality with Applications in Quantum Estimation

Article

DOI: 10.1007/s00220-014-2059-0

Cite this article as:
Marvian, I. & Spekkens, R.W. Commun. Math. Phys. (2014) 331: 431. doi:10.1007/s00220-014-2059-0
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Abstract

Schur–Weyl duality is a powerful tool in representation theory which has many applications to quantum information theory. We provide a generalization of this duality and demonstrate some of its applications. In particular, we use it to develop a general framework for the study of a family of quantum estimation problems wherein one is given n copies of an unknown quantum state according to some prior and the goal is to estimate certain parameters of the given state. In particular, we are interested to know whether collective measurements are useful and if so to find an upper bound on the amount of entanglement which is required to achieve the optimal estimation. In the case of pure states, we show that commutativity of the set of observables that define the estimation problem implies the sufficiency of unentangled measurements.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  3. 3.Department of Physics and Astronomy, Center for Quantum Information Science and TechnologyUniversity of Southern CaliforniaLos AngelesUSA

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