Distribution of high-dimensional entanglement via an intra-city free-space link

Abstract

Quantum entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Increasing the dimensionality of entanglement has been shown to improve robustness and channel capacities in secure quantum communications. Here we report on the distribution of genuine high-dimensional entanglement via a 1.2-km-long free-space link across Vienna. We exploit hyperentanglement, that is, simultaneous entanglement in polarization and energy-time bases, to encode quantum information, and observe high-visibility interference for successive correlation measurements in each degree of freedom. These visibilities impose lower bounds on entanglement in each subspace individually and certify four-dimensional entanglement for the hyperentangled system. The high-fidelity transmission of high-dimensional entanglement under real-world atmospheric link conditions represents an important step towards long-distance quantum communications with more complex quantum systems and the implementation of advanced quantum experiments with satellite links.

Figure 1. Illustration of the high-dimensional entanglement distribution experiment.

A hyperentangled photon source was located in a laboratory at the IQOQI Vienna. The source utilized SPDC in a periodically poled KTiOPO₄ (ppKTP) crystal, which was placed at the centre of a Sagnac interferometer and pumped with a continuous-wave 405-nm laser diode (LD). The polarization/energy–time hyperentangled photon pairs had centre wavelengths of λ_B∼780 nm and λ_A∼840 nm, respectively. Photon A was sent to Alice at IQOQI using a short fibre link, while photon B was guided to a transmitter telescope on the roof of the institute and sent to Bob at the BOKU via a 1.2-km-long free-space link. At Bob, the photons were collected using a large-aperture telephoto objective with a focal length of 400 mm. The 532-nm beacon laser was separated from the hyperentangled photons using a dichroic mirror and focused onto a CCD image sensor to maintain link alignment and to monitor atmospheric turbulence. Alice’s and Bob’s analyser modules allowed for measurements in the polarization or energy–time basis. The polarization was analysed using a half-wave plate (HWP) and a polarizing beam splitter (PBS) with a single-photon avalanche diode (SPAD) in each output port. An additional phase shift could be introduced in Alices measurement module by tilting a birefringent crystal about its optical axis. In both analyser modules, optional calcite crystals could be added before the PBS to introduce the polarization-dependent delay required for Franson interference measurements in the energy–time basis. Single-photon detection events were recorded with a GPS-disciplined time tagging unit (TTU) and stored on local hard drives for post processing. Bob’s measurement data were streamed to Alice via a classical WiFi link to identify photon pairs in real time. Map data ©2017 Google.

Figure 2. Transmission rate and clock drift.

(a) Average single-photon (blue line) and two-photon (red line) detection rate (100 ms integration time) after 1.2-km-long free-space transmission. The short-term signal fluctuated due to atmospheric turbulence, whereas the time-averaged rate of ∼20 kcps remained almost constant over several hours. (b) Relative clock drift between Alice and Bob. The inset depicts the normalized histogram of two-photon detection events in 80 ps time bins centred around the flight-time offset of ∼3.94 μs. All data acquired for night-time operation on 25–26 April 2016.

Figure 3. Experimental characterization of hyperentanglement.

Two-photon correlation functions in the polarization basis (a) and energy–time basis (b) as a function of the variable phase shift introduced in Alice’s measurement module. Each data point was evaluated from two-photon detection events accumulated over a 10 s integration time, without subtraction of accidental counts. The error bars that denote the 3-σ s.d. due to Poissonian count statistics are smaller than the data markers. The best fit functions (least-mean-square fit to the expected two-photon correlation in presence of experimental imperfections) exhibit visibilities in the polarization basis (blue line) and in the energy–time basis (orange line). Almost no interference was observed when the energy–time to polarization transfer set-up was introduced in Alice’s detection module only (yellow line, ).

Figure 4. Energy–time to polarization transfer set-up.

The calcite crystal acts as an unbalanced polarization interferometer, which introduces a time shift of τ>t_c between vertically (V) and horizontally (H) polarized photons. After the transfer set-up polarization measurements in a superposition basis allow to probe energy–time coherence (see also Supplementary Discussion).