Random numbers are a valuable component in diverse applications that range from simulations(1) over gambling to cryptography(2,3). The quest for true randomness in these applications has engendered a large variety of different proposals for producing random numbers based on the foundational unpredictability of quantum mechanics(4-11). However, most approaches do not consider that a potential adversary could have knowledge about the generated numbers, so the numbers are not verifiably random and unique(12-15). Here we present a simple experimental setup based on homodyne measurements that uses the purity of a continuous-variable quantum vacuum state to generate unique random numbers. We use the intrinsic randomness in measuring the quadratures of a mode in the lowest energy vacuum state, which cannot be correlated to any other state. The simplicity of our source, combined with its verifiably unique randomness, are important attributes for achieving high-reliability, high-speed and low-cost quantum random number generators

Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81-0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown

We demonstrate for the first time the feasibility of free space quantum key distribution with continuous variables under real atmospheric conditions. More specifically, we transmit coherent polarization states over a 100 m free space channel on the roof of our institute's building. In our scheme, signal and local oscillator are combined in a single spatial mode which autocompensates atmospheric fluctuations and results in an excellent interference. Furthermore, the local oscillator acts as spatial and spectral filter thus allowing unrestrained daylight operation.

We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon-number-resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, prove to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.