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

By Eric Chitambar, Debbie W. Leung, L. Mančinska, Maris A. Ozols, Andreas J. Winter. 2012

466 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/2710793dbf83b6739748042c718d6b0d2c543ae3

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum resource theories (2018, background): “However, LOCC is not a closed set of operations in the sense that there exists sequences of protocols, each increasing in round number, that converge to a map which cannot be implemented by either finite-round or unboundedround LOCC (Chitambar et al., 2012, 2014).”
Entanglement certification from theory to experiment (2018, background): “Because each of these pure states is separable, mixed separable states can easily be prepared by coordinated local operations, that is, local operations and classical communication (LOCC) [43, 44].”
Quantum channels and memory effects (2012, background): “An important class of bipartite quantum channels are finally those that can be simulated only with local operations and classical communication (LOCC), see (Chitambar et al., 2012) for a recent survey.”
The Theory of Quantum Information (2018, background): “It is known that the set of LOCC channels, as they have been defined in this chapter, is generally not closed for a fixed choice of spaces; this was proved (for bipartite channels) by Chitambar, Leung, Mančinska, Ozols, and Winter [49].”