On-chip generation of high-order single-photon W-states

Journal name:
Nature Photonics
Year published:
Published online
Corrected online


Quantum superposition is the quantum-mechanical property of a particle whereby it inhabits several of its possible quantum states simultaneously. Ideally, this permissible coexistence of quantum states, as defined on any degree of freedom, whether spin, frequency or spatial, can be used to fully exploit the information capacity of the associated physical system. In quantum optics, single photons are the quanta of light, and their coherence properties allow them to establish entangled superpositions between a large number of channels, making them favourable for realizations of quantum information processing schemes. In particular, single-photon W-states (that is, states exhibiting a uniform distribution of the photons across multiple modes) represent a class of multipartite maximally-entangled quantum states that are highly robust to dissipation. Here, we report on the generation and verification of single-photon W-states involving up to 16 spatial modes, and exploit their underlying multi-mode superposition for the on-chip generation of genuine random numbers.

At a glance


  1. Schematic of the experimental set-up.
    Figure 1: Schematic of the experimental set-up.

    A heralded single-photon source at a wavelength of 815 nm was implemented by means of spontaneous parametric downconversion from a pump laser at 407.5 nm. Photons emerging at the output of the device were collected via a fibre array and subsequently fed into single-photon detectors (avalanche photodiodes, APDs) triggered by the herald.

  2. Generation of high-order photonic W-states on an integrated platform.
    Figure 2: Generation of high-order photonic W-states on an integrated platform.

    a, Odd number N of entangled channels. Here, the state is obtained through the coherent evolution of a single photon injected into the central site of a lattice comprising N identical waveguides. Appropriately engineered couplings continuously transform the initially localized photon into the desired equal superposition of all N channels after distance zW. Subsequently, a fan-out section designed to arrest the propagation dynamics serves as an interface to the output ports. b, Even number N of entangled channels. A hierarchical network of 50/50 couplers transforms the single-photon input state into W-states of order N = 2m, where m is the number of sequential couplers. The specific structure shown here is capable of producing any of states , and , depending on the choice of input port. c, Experimentally obtained probability distributions of states and . In the N = 5 case, the length of the functional section was zW = 5 cm. The system used to synthesize the N = 16 state consisted of a pair of realizations of the structure in b arranged in parallel horizontal planes and connected to the input by a vertical 50/50 coupler. Standard deviations (from the uniform distribution) of the individual measurements are shown as horizontal bars.

  3. Interferometric validation of W-states, given a priori knowledge of a single-photon input state.
    Figure 3: Interferometric validation of W-states, given a priori knowledge of a single-photon input state.

    a, To demonstrate coherence between the outputs of the N = 5 device, we allowed the created state to undergo interference while propagating through a second section of length zW before separating the channels in the fan-out arrangement. b, Theoretical probability distributions (top row) assuming coherent (left) or fully incoherent (right) conditions at the end of the functional section. The measured interferogram (bottom, left) proves a coherent superposition of the channels, that is, state . As a comparison, the incoherent case, with its characteristic absence of interference, was observed by subsequently launching single photons into each channel of the array (alternating colour) and adding the probability distributions, incoherently (bottom right). c, In the N = 8 case, an additional sequence of integrated 50/50 couplers were attached to verify entanglement of the output. d, The theoretical output probability distribution of this arrangement under perfect conditions exhibits a projection to only one output (top); the experimental results clearly exceed the required fidelity condition of 7/8 (bottom).

Change history

Corrected online 18 September 2014
In the version of this Article originally published, the contribution of Demetrios N. Christodoulides to conceiving the idea behind the work was not acknowledged in the Author Contributions section. This error has now been corrected in the HTML and PDF versions of the Article.


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Author information

  1. These authors contributed equally to this work

    • Markus Gräfe,
    • René Heilmann &
    • Armando Perez-Leija


  1. Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, Jena 07743, Germany

    • Markus Gräfe,
    • René Heilmann,
    • Armando Perez-Leija,
    • Robert Keil,
    • Felix Dreisow,
    • Matthias Heinrich,
    • Stefan Nolte &
    • Alexander Szameit
  2. Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria

    • Robert Keil
  3. CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, Florida 32816, USA

    • Matthias Heinrich &
    • Demetrios N. Christodoulides
  4. INAOE, Coordinacion de Optica, Luis Enrique Erro No. 1, Tonantzintla, Puebla 72840, Mexico.

    • Hector Moya-Cessa


M.G., R.H., A.P.-L. and D.N.C. conceived the idea. M.G., R.H and R.K. designed the samples and performed the measurements. A.P.-L., M.G., R.H and R.K. analysed the data. A.S. supervised the project. All authors discussed the results and co-wrote the manuscript.

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The authors declare no competing financial interests.

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