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

Eric Chitambar, Debbie Leung, Laura Mančinska, Maris Ozols, Andreas Winter

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)303-326
Number of pages24
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Mar 19 2014
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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