Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit

Journal name:
Nature Photonics
Year published:
Published online


Entanglement is the quintessential quantum-mechanical phenomenon understood to lie at the heart of future quantum technologies and the subject of fundamental scientific investigations. Mixture, resulting from noise, is often an unwanted result of interaction with an environment, but is also of fundamental interest, and is proposed to play a role in some biological processes. Here, we report an integrated waveguide device that can generate and completely characterize pure two-photon states with any amount of entanglement and arbitrary single-photon states with any amount of mixture. The device consists of a reconfigurable integrated quantum photonic circuit with eight voltage-controlled phase shifters. We demonstrate that, for thousands of randomly chosen configurations, the device performs with high fidelity. We generate maximally and non-maximally entangled states, violate a Bell-type inequality with a continuum of partially entangled states, and demonstrate the generation of arbitrary one-qubit mixed states.

At a glance


  1. A two-photon reconfigurable quantum circuit for generating, manipulating and detecting entanglement and mixture.
    Figure 1: A two-photon reconfigurable quantum circuit for generating, manipulating and detecting entanglement and mixture.

    a, Quantum circuit diagram consisting of pairs of Hadamard-like gates H′ = eiπ/2   · H (where H is the usual Hadamard gate) and Rz(φ=  rotations, that together implement Ûi,f(φj, φk), and two H′ gates and a controlled-SIGN or CZ gate, that together implement a CNOT. b, Waveguide implementation of the circuit composed of directional couplers and voltage-controlled thermo-optic phase shifters (marked as orange triangles). Directional couplers with splitting ratio η = 1/3 are marked as dots; all other couplers have η = 1/2.

  2. Classical and quantum interference fringes.
    Figure 2: Classical and quantum interference fringes.

    a, Interference fringe measured at the two outputs of a single MZ interferometer on the chip. Experimental data are presented as black circles. Solid lines show fits. b, HOM dip, measured using a single MZ interferometer as a beamsplitter. Two-photon coincidence counts are shown as black circles. The red line shows a fit to these data with Gaussian and sinc components, due to quantum interference and determined by the spectral filters used, and a linear term accounting for slight decoupling of the source. The blue line shows a fit to the measured rate of accidental coincidences, with Gaussian and linear components. Error bars in both figures assume Poissonian statistics.

  3. Statistical fidelity of photon coincidence count rates.
    Figure 3: Statistical fidelity of photon coincidence count rates.

    The histogram shows the distribution of statistical fidelity between ideal and measured coincidence probabilities, over 995 sets of eight randomly selected phases . 96% of phase settings produced statistics corresponding with theory to f > 0.97.

  4. Bell states generated and characterized on-chip.
    Figure 4: Bell states generated and characterized on-chip.

    ad, Real parts of the density operators of the Bell states |Φ+right fence, |Φright fence, |Ψ+right fence and |Ψright fence (a,b,c,d, respectively).

  5. CHSH manifold.
    Figure 5: CHSH manifold.

    a, The Bell–CHSH sum S, plotted as a function of phases α and β. In the α-axis, the state shared between Alice and Bob is tuned continuously between product states at α = 0, π and maximally entangled states at α = π/2, 3π/2. The β-axis shows S as a function of Bob's variable measurements, which can be thought of as two operator axes in the real plane of the Bloch sphere, fixed with respect to each other at an angle of π/2 but otherwise free to rotate with angle β between 0 and 2π. The blue curves show a projection of the manifold onto each axis. Yellow contours mark the edges of regions of the manifold that violate −2 ≤ S ≤ 2. Red lines on the axes also show this limit. b, Experimentally measured manifold. Data points are drawn as black circles. Data points that violate the CHSH inequality are drawn as yellow circles. The surface shows a fit to the experimental data.

  6. Histogram showing the statistical distribution of quantum-state fidelity between 119 randomly chosen single-qubit target states and the corresponding mixed states generated and characterized on-chip.
    Figure 6: Histogram showing the statistical distribution of quantum-state fidelity between 119 randomly chosen single-qubit target states and the corresponding mixed states generated and characterized on-chip.

    Inset: Ψ drawn in the Bloch sphere using 63 mixed states, again generated and characterized on-chip. These states are chosen from the real plane of the sphere for clarity. Note that each point is derived from a different bipartite partially entangled state.


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Author information


  1. Centre for Quantum Photonics, H. H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol BS8 1UB, UK

    • P. J. Shadbolt,
    • M. R. Verde,
    • A. Peruzzo,
    • A. Politi,
    • A. Laing,
    • M. Lobino,
    • J. C. F. Matthews,
    • M. G. Thompson &
    • J. L. O'Brien


All authors contributed extensively to the work presented in this paper.

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The authors declare no competing financial interests.

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