Testing microscopic discretization

Miguel Navascues, David Perez-Garcia, Ignacio Villanueva

Research output: Contribution to journalArticle (Academic Journal)

Abstract

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.
Original languageEnglish
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number085304
Publication statusPublished - 11 Feb 2013

Bibliographical note

Proof of strong NP-hardness. Connection with random walks. New asymptotic results. Numerous typos corrected

Keywords

  • math.PR
  • quant-ph

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