Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference

Karol Bartkiewicz, Grzegorz Chimczak, and Karel Lemr
Phys. Rev. A 95, 022331 – Published 22 February 2017

Abstract

We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of nine Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate both that these invariants are a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.

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  • Received 8 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.022331

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Karol Bartkiewicz1,2,*, Grzegorz Chimczak1, and Karel Lemr2

  • 1Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland
  • 2RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Academy of Sciences of the Czech Republic, 17. Listopadu 12, 772 07 Olomouc, Czech Republic

  • *bark@amu.edu.pl

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Vol. 95, Iss. 2 — February 2017

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