Security of Plug-and-Play QKD Arrangements with Finite Resources

The security of a passive plug-and-play QKD arrangement in the case of finite (resources) key lengths is analysed. It is assumed that the eavesdropper has full access to the channel so an unknown and untrusted source is assumed. To take into account the security of the BB84 protocol under collective attacks within the framework of quantum adversaries, a full treatment provides the well-known equations for the secure key rate. A numerical simulation keeping a minimum number of initial parameters constant as the total error sought and the number of pulses is carried out. The remaining parameters are optimized to produce the maximum secure key rate. Two main strategies are addressed: with and without two-decoy-states including the optimization of signal to decoy relationship

Low-complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analysed: firstly, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.Comment: IEEE Transactions on Signal Processing, accepted for publication. Article in pres

Accuracy requirements to test the applicability of the random cascade model to supersonic turbulence

A model, which is widely used for inertial rang statistics of supersonic turbulence in the context of molecular clouds and star formation, expresses (measurable) relative scaling exponents Z_p of two-point velocity statistics as a function of two parameters, beta and Delta. The model relates them to the dimension D of the most dissipative structures, D=3-Delta/(1-beta). While this description has proved most successful for incompressible turbulence (beta=Delta=2/3, and D=1), its applicability in the highly compressible regime remains debated. For this regime, theoretical arguments suggest D=2 and Delta=2/3, or Delta=1. Best estimates based on 3D periodic box simulations of supersonic isothermal turbulence yield Delta=0.71 and D=1.9, with uncertainty ranges of Delta in [0.67, 0.78] and D in [2.04,1.60]. With these 5-10\% uncertainty ranges just marginally including the theoretical values of Delta=2/3 and D=2, doubts remain whether the model indeed applies and, if it applies, for what values of beta and Delta. We use a Monte Carlo approach to mimic actual simulation data and examine what factors are most relevant for the fit quality. We estimate that 0.1% (0.05%) accurate Z_p, with p=1...5, should allow for 2% (1%) accurate estimates of beta and Delta in the highly compressible regime, but not in the mildly compressible regime. We argue that simulation-based Z_p with such accuracy are within reach of today's computer resources. If this kind of data does not allow for the expected high quality fit of beta and Delta, then this may indicate the inapplicability of the model for the simulation data. In fact, other models than the one we examine here have been suggested.Comment: 8 pages, 8 figures, accepted by Astronomy and Astrophysic

Programmable coherent linear quantum operations with high-dimensional optical spatial modes

A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally complete positive operator-valued measures (SIC POVMs) are implemented with dimensionality of 15. The matrix fidelity of QFT is 0.85, while the statistical fidelity of SIC POVMs and fidelity of QST are ~0.97 and up to 0.853, respectively. We believe that our device has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down conversion in nonlinear crystals