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Quantum Measurements

Quantum random number generator

Quantum random number generators have the potential to deliver truly random numbers, an important attribute for many applications ranging from simulations over gambling to cryptography. Our random number generator [1] measures the noise of the electric field variables of a vacuum state. This can be realized with a simple homodyne setup. By appropriately post-processing the measured date, truly random numbers which are solely based on quantum noise can be extracted. Samples of our truly random numbers can be downloaded here: 50MB, 200MB

Involved in this project is:
Christian Gabriel,   Christoffer Wittmann,   Denis Sych ,   Ruifang Dong,   Christoph Marquardt,   Gerd Leuchs

Christian Gabriel, Christoffer Wittmann, Denis Sych, Ruifang Dong, Wolfgang Mauerer, Ulrik L. Andersen, Christoph Marquardt, Gerd Leuchs

Artists' illustration of the continuous variable quantum random number generator. Design by Michael Förtsch.

Tomography of polarization squeezed states

Polarization states of the light field are conveniently described in the Stokes space, which is spanned by the Stokes vectors. In the quantum mechanical treatment, the Stokes space is not continuous, but is composed of a set of nested spheres. A polarization state is generally distributed over several of these spheres. However, in the case of a bright and localized state, the state can be approximated to lie in a quasi-continuous and flat space.

We could show explicitly that the state reconstruction is then equivalent to the inverse Radon transformation from projections of the state along all directions in Stokes space. This technique, however, is statistically unstable and is likely to produce unphysical features in the reconstructed state. As an alternative, we have proposed a novel maximum likelihood reconstruction (ML) and compared the two techniques for the reconstruction of a bright polarization squeezed state [1]. A visual perspective of how we perform this reconstruction can be obtained from the video abstract shown on the right.
Video abstract: Quantum polarization tomography of bright squeezed light

Thereby, we could show that the ML technique allows us to get
reconstructions of the same quality but from data sets which are two orders
of magnitude smaller than required for the inverse Radon reconstruction.
The results of the technique are shown in the figure below.

Involved in this project are:
Christian Mueller
,   Christoph Marquardt,   Gerd Leuchs

[1] C. R. Müller, B. Stoklasa, C. Peuntinger, C. Gabriel, J. Řeháček, Z. Hradil, A. B. Klimov, G. Leuchs, Ch. Marquardt, and L. L. Sánchez-Soto,
New Journal of Physics 14, 085002 (2012)

Fig. 2: Views on the reconstructed coherent (blue) and squeezed (orange) polarization states.

Novel quantum receivers

Fig. 3: Scheme for discriminating quadrature phase-shift keyed quantum signals

Quantum state discrimination is one of the fundamental issues in optical communication and quantum signal detection. An important figure of merit here is the error rate. For a pair of coherent states, homodyne detection represents an effective way to achieve near-minimal error discrimination. A receiver based on photon counting would lead to even smaller error rates, provided if signal intensities are sufficiently large. In order to outperform the homodyne scheme also for smaller photon numbers, we have succesfully implemented a novel detection schemes [1–4]. 

In our latest work on quantum state discrimination, we experimentally demonstrated a hybrid discrimination scheme for quadrature phase-shift keyed quantum signals (QPSK) which outperforms the standard scheme – heterodyne detection – for any signal power [5]. The QPSK alphabet comprises four states with identical amplitude but separated by a relative phase shift of π/2 and is used for instance by the HSDPA protocol in UMTS networks for mobile phones, in digital satellite communication and in backbone fiber networks.
For the identification of the input state, the signal is divided on a beam splitter and the parts are guided to a homodyne receiver and a photon detector, respectively. First, the homodyne detector performs an adequate quadrature measurement that allows to discard half of the candidate states. The result is forwarded to a second receiver stage where it is used to optimally tune a displacement prior to a photon detector which finally discriminates between the remaining pair of states.
Interestingly, the discrimination in our scheme is carried out by a hybrid receiver addressing both the continuous variable (homodyne detection) and the discrete variable (photon detection) representation of the signal states.

Involved in this project are:
Christian Müller
,   Christoffer Wittmann,   Christoph Marquardt,   Gerd Leuchs

[1] C. Wittmann, M. Takeoka, Katiuscia N. Cassemiro, M. Sasaki, G. Leuchs,
     and U. L. Andersen,
     Phys. Rev. Lett 101, 210501-4 (2008). [preprint]

[2] C. Wittmann, U. L. Andersen, and G. Leuchs,
     J. Mod. Opt. 57, 213 (2010). [preprint]

[3] C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and
     G. Leuchs,
     Phys. Rev. Lett 104, 100505  (2010). [preprint]

[4] C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and
     G. Leuchs,
     Phys. Rev. A 81, 062338  (2010). [preprint]

[5] C. R. Müller, M. A. Usuga, C. Wittmann, M. Takeoka, Ch. Marquardt,
     U. L.
Andersen, and, G. Leuchs,
     New Journal of Physics 14, 083009 (2012). [preprint]