Continuous-variable quantum key distribution has made great progress during the last years. Recently, a security proof for a finite number of measurements with composable security against arbitrary attacks was published [1] which employs Einstein-Podolsky-Rosen (EPR) entangled states. Here, we present the first implementation of this protocol, demonstrating the feasibility of secure key generation. The implementation relies on continuous-wave quadrature-entangled states at the telecommunication wavelength of 1550 nm with unprecedented EPR entanglement and homodyne detection with a random choice of quadrature for each measurement. We further present the generation of a key which is secure under collective attacks with 10⁸ measurements.

[1] F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, Physical Review Letters 109, 100502 (2012).

The ability to reduce proofs of quantum information processing tasks from any permutation in-variant state to a de-Finetti state, that is, a convex combination of i.i.d. states, is useful in several tasks, such as cryptographic quantum protocols and quantum tomography. It is thus interesting to see whether such de-Finetti type theorems are unique for quantum theory or can be proven for more general theories. We prove that this can indeed be done under the framework of conditional probability distributions. That is, a physical system is described by a conditional probability distribution PA|X where X denotes the possible measurements and A the possible outcomes. For such systems we prove a post selection theorem which states that any permutation invariant system PA|X can be post selected by a measurement of a de-Finetti type system with high enough probability. We use this theorem to simplify security proofs of non-signalling cryptographic protocols.

If two parties were to exploit today’s quantum key distribution (QKD) systems, they would be limited to being at most ~100 km apart [1]. It is possible to overcome this limit with a quantum repeater that exploits quantum memories for qubit synchronization [1]. Among other criteria desired for quantum memories, simultaneous storage of multiple qubits (multiplexing) and recall of any desired qubit on-demand is required for a quantum repeater [1,2]. These properties are generally associated with the ability to trigger the re-emission of any previously stored qubit at a desired time [3]. We will argue that this view is too restricted, and that it is possible to build a quantum repeater using quantum memories that allow storage of frequency multiplexed qubits supplemented with frequency-selective read-out on demand. Furthermore we report on measurements exploiting the atomic frequency comb protocol in a Ti:Tm:LiNbO3 waveguide cooled to 3 K [4,5] that shows the required on-demand readout with average fidelities of 0.95 ± 0.03 thereby significantly violating the maximum fidelity of 0.67 possible using a classical memory. Our demonstration constitutes an important step towards the development of a quantum repeater.
[1] N. Sangouard et al., Reviews of Modern Physics 83, 33 (2011).
[2] A. I. Lvovsky, W. Tittel, and B.C. Sanders, Nature Photonics 3, 706 (2009).
[3] C. Simon et al., Phys. Rev. Lett. 98, 190503 (2007).
[4] M. Afzelius et al., Phys. Rev. A 79, 052329 (2009).
[5] E. Saglamyurek et al., Nature 469, 512 (2011).