Quantum mutual information of an entangled state propagating through a fast-light medium

Journal name:
Nature Photonics
Year published:
Published online

It is widely accepted that information cannot travel faster than c, the speed of light in vacuum1, 2, 3. Here, we investigate the behaviour of quantum correlations and information in the presence of dispersion. To do so we send one half of an entangled state of light through a gain-assisted slow- or fast-light medium and detect the transmitted quantum correlations and quantum mutual information4, 5, 6. We show that quantum correlations can be advanced by a small fraction of the correlation time, even in the presence of noise added by phase-insensitive gain. Additionally, although the peak of the quantum mutual information between the modes can be advanced, we find that the degradation of the mutual information due to added noise appears to prevent an advancement of the leading edge. In contrast, we demonstrate a significant delay of both the leading and trailing edges of the mutual information in a slow-light system.

At a glance


  1. Experimental set-up.
    Figure 1: Experimental set-up.

    a,b, Vacuum-squeezed twin beams are generated in cell 1 using 4WM in a double-lambda configuration (b). A region of anomalous dispersion for the conjugate is created in a second vapour cell using a second 4WM process driven by pump 2, whose frequency is independently tunable with respect to pump 1 (Supplementary Section 1). The phase of the local oscillators (LOs) is scanned using piezo-electric transducers (PZTs) to verify the presence of entanglement. The sum and difference signals of the homodyne detections are recorded on a pair of spectrum analysers (SAs) to detect quantum correlations. An oscilloscope is triggered to detect time traces of the individual homodyne detectors given a predetermined threshold of squeezing heralded by the SAs. c, Measured gain profile (black solid line) of the second 4WM process as a function of the detuning of pump 2 relative to pump 1. From the gain profile, we numerically compute the associated refractive index n(ω) and group index ng. In determining the advancement, we confine our attention to fluctuations in the frequency band (shaded green) where we observe quantum correlations generated in cell 1. We tune the second pump frequency so that the bandwidth of anomalous dispersion coincides with the bandwidth where we observe quantum correlations.

  2. Persistence of correlations associated with entanglement in the presence of anomalous dispersion.
    Figure 2: Persistence of correlations associated with entanglement in the presence of anomalous dispersion.

    a, We observe up to −3 dB of squeezing with an associated inseparability when the second (fast-light) 4WM process is suppressed. b, In the presence of a small phase-insensitive gain giving rise to anomalous dispersion, the squeezing reduces to −2.3 dB and increases to 1.2, which is still sufficient to show entanglement . c, Average normalized cross-correlation functions for the correlated and anti-correlated joint quadratures. The left axis applies to the reference and advanced curves for the correlated quadratures, and the right axis applies to the anti-correlated quadratures (indicated by arrows). When calculating the cross-correlation functions, the reference and fast-light data are both subject to the same passband filter used to calculate (Supplementary Sections 3.1 and 3.2). d,e, Closer looks at the peak correlation (d) and anti-correlations (e) portrayed in c.

  3. Observed advance in the quantum correlations.
    Figure 3: Observed advance in the quantum correlations.

    a, Average advance and accompanying degradation of the inseparability, ( implies entanglement), in the presence of anomalous dispersion (fast, red curves) and upon blocking the second pump (reference, black curves). The subpanel provides a closer look at the minima of the inseparability curves. b, Sampling of the squeezing versus delay over 200 experimental iterations used to compute the average . c, Histogram of the sampled minima of the joint quadrature noise (that is, maximum squeezing) versus the relative probe–conjugate delay. From the sampled shots we extract an advance of 3.7 ± 0.1 ns, where the uncertainty has been estimated by computing the standard deviation of the mean.

  4. Comparison of computed quantum mutual information between the c.w. probe and conjugate as a function of relative delay for fast and slow light.
    Figure 4: Comparison of computed quantum mutual information between the c.w. probe and conjugate as a function of relative delay for fast and slow light.

    The smooth shape of the curves results from the large amount of data (180 files consisting of 1 × 107 points per file) used to calculate the mutual information. When considering fast-light advancement of the conjugate (red trace), we observe an advance in the peak of the mutual information of 3.7 ± 0.1 ns. The subpanel provides a closer look at the maxima of the mutual information curves for the reference and fast-light cases. There is no statistically significant advance of the leading edge of the mutual information in the case of fast-light propagation. Repeating the same analysis for slow-light propagation of the probe we observe significant delays of both the leading and trailing edges of the mutual information (green trace).


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Author information


  1. Quantum Measurement Division, National Institute of Standards and Technology and Joint Quantum Institute, NIST & the University of Maryland, Gaithersburg, Maryland 20899, USA

    • Jeremy B. Clark,
    • Ryan T. Glasser,
    • Quentin Glorieux,
    • Tian Li &
    • Paul D. Lett
  2. Laboratoire Kastler Brossel, Université Pierre et Marie Curie, Ecole Normale Supérieure and CNRS, UPMC Case 74, 4 place Jussieu, 75252 Paris Cedex 05, France

    • Quentin Glorieux
  3. Max Planck Institute for the Science of Light, Günther–Scharowsky–Strasse 1, Building 24, 91058 Erlangen, Germany

    • Ulrich Vogl
  4. Physics Department, Williams College, Williamstown, Massachusetts 01267, USA

    • Kevin M. Jones


J.B.C., R.T.G., Q.G. and U.V. analysed the data. J.B.C., R.T.G., U.V. and P.D.L. conceived and designed the experiments. J.B.C., R.T.G., Q.G. and U.V. contributed materials and analysis tools. J.B.C., R.T.G., Q.G., U.V. and T.L. performed the experiments. J.B.C., R.T.G., Q.G., U.V., K.M.J. and P.D.L. wrote the paper.

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