• Open Access

Experimental Determination of Multipartite Entanglement with Incomplete Information

G. H. Aguilar, S. P. Walborn, P. H. Souto Ribeiro, and L. C. Céleri
Phys. Rev. X 5, 031042 – Published 24 September 2015

Abstract

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation, and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for nonpure states or nonideal measurement conditions.

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  • Received 7 December 2014

DOI:https://doi.org/10.1103/PhysRevX.5.031042

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

G. H. Aguilar1,*, S. P. Walborn1,†, and P. H. Souto Ribeiro2,‡

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, Rio de Janeiro 21945-970, Brazil
  • 2Departamento de Fisica, Universidade Federal de Santa Catarina, Caixa Postal 476, 88040-900 Florianopolis, Santa Catarina, Brazil

L. C. Céleri3,§

  • 3Instituto de Física, Universidade Federal de Goiás, Goiânia, 74001-970 Goiás, Brazil

  • *gabo@if.ufrj.br
  • swalborn@if.ufrj.br
  • p.h.s.ribeiro@ufsc.br
  • §lucas@chibebe.org

Popular Summary

Entanglement is a property of quantum objects in which their state cannot simply be described by the sum of the individual states of their components. One difficulty faced in the study of the fundamental properties of entangled states is that the mathematical complexity of the description increases exponentially with the number of entangled subsystems. Moreover, experimental procedures to reconstruct an entangled state may require an enormous number of measurements, which necessitates a significant amount of resources and time. For instance, the reconstruction of a quantum state with five subsystems requires approximately one thousand measurements, and the reconstruction of a quantum state with ten subsystems requires more than one million measurements. Furthermore, the fragility of a quantum state increases with the number of subsystems, making the complete characterization of these systems practically impossible. Here, we test a novel idea of how to partially characterize a multipartite quantum state with a reduced number of measurements in the laboratory.

We employ an optical setup in which photon pairs are generated using a 325-nm laser to create three- and four-partite states. We find that the number of measurements required scales only linearly with the number of subsystems instead of exponentially, as in the case of a full characterization. Our method is based on the reconstruction of the local states of the subsystems without measuring the correlations between them. Surprisingly, in many cases, it is still possible to determine if the state exhibits genuine multipartite entanglement. We prepare and test quantum states of photons pertaining to different classes of entanglement. We find that this local characterization works not only for the ideal case of pure states but also for states that are moderately mixed because of experimental noise.

We expect that this type of partial characterization will be useful for quantum information applications that use certain entangled states as a resource.

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Vol. 5, Iss. 3 — July - September 2015

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