Communications in Mathematical Physics

, Volume 328, Issue 1, pp 303–326 | Cite as

Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)

  • Eric Chitambar
  • Debbie Leung
  • Laura Mančinska
  • Maris Ozols
  • Andreas Winter
Article

Abstract

In this paper we study the subset of generalized quantum measurements on finite dimensional systems known as local operations and classical communication (LOCC). While LOCC emerges as the natural class of operations in many important quantum information tasks, its mathematical structure is complex and difficult to characterize. Here we provide a precise description of LOCC and related operational classes in terms of quantum instruments. Our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds. While the set of LOCC is not topologically closed, we show that finite round LOCC constitutes a compact subset of quantum operations. Additionally we show the existence of an open ball around the completely depolarizing map that consists entirely of LOCC implementable maps. Finally, we demonstrate a two-qubit map whose action can be approached arbitrarily close using LOCC, but nevertheless cannot be implemented perfectly.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Eric Chitambar
    • 1
    • 2
  • Debbie Leung
    • 3
  • Laura Mančinska
    • 3
  • Maris Ozols
    • 3
    • 4
  • Andreas Winter
    • 5
    • 6
    • 7
    • 8
  1. 1.Department of PhysicsSouthern Illinois UniversityCarbondaleUSA
  2. 2.The Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Department of Combinatorics and Optimization, Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  4. 4.IBM TJ Watson Research CenterYorktown HeightsUSA
  5. 5.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  6. 6.Física Teòrica: Informació i Fenomens QuànticsUniversitat Autònoma de BarcelonaBellaterraSpain
  7. 7.Department of MathematicsUniversity of BristolBristolUK
  8. 8.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore

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