On the properties of Circular-Beams

Circular-Beams were introduced as a very general solution of the paraxial wave equation carrying Orbital Angular Momentum. Here we study their properties, by looking at their normalization and their expansion in terms of Laguerre-Gauss modes. We also study their far-field divergence and, for particular cases of the beam parameters, their possible experimental generation.Comment: 5 page

The role of beam waist in Laguerre-Gauss expansion of vortex beam

Laguerre-Gauss (LG) modes represent an orthonormal basis set of solutions of the paraxial wave equation. LG are characterized by two integer parameters $n$ and $\ell$ that are related to the radial and azimuthal profile of the beam. The physical dimension of the mode is instead determined by the beam waist parameter $w_0$: only LG modes with the same $w_0$ satisfy the orthogonality relation. Here, we derive the scalar product between two LG modes with different beam waists and show how this result can be exploited to derive different expansions of a generic beam in terms of LG modes. In particular, we apply our results to the recently introduced Circular Beams, by deriving a previously unknown expansion. We finally show how the waist parameter must be chosen in order to optimize such expansion.Comment: 5 page

EPR-steering: closing the detection loophole with non-maximally entangled states and arbitrary low efficiency

Quantum steering inequalities allow to demonstrate the presence of entanglement between two parties when one of the two measurement device is not trusted. In this paper we show that quantum steering can be demonstrated for arbitrary low detection efficiency by using two-qubit non-maximally entangled states. Our result can have important applications in one-sided device-independent quantum key distribution.Comment: Revtex, 5 pages, 3 figure

Strong measurements give a better direct measurement of the quantum wave function

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wavefunction [Nature (London) 474, 188 (2011)]. Here we show that direct measurement of the wavefunction can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e. those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the reconstructed and original wavefunctions obtained by the weak measurement approach: this will allow to define the range of applicability of such method.Comment: Updated version, 5 pages + Supplementary Informatio

Random bits, true and unbiased, from atmospheric turbulence

Random numbers represent a fundamental ingredient for numerical simulation, games, informa- tion science and secure communication. Algorithmic and deterministic generators are affected by insufficient information entropy. On the other hand, suitable physical processes manifest intrinsic unpredictability that may be exploited for generating genuine random numbers with an entropy reaching the ideal limit. In this work, we present a method to extract genuine random bits by using the atmospheric turbulence: by sending a laser beam along a 143Km free-space link, we took advantage of the chaotic behavior of air refractive index in the optical propagation. Random numbers are then obtained by converting in digital units the aberrations and distortions of the received laser wave-front. The generated numbers, obtained without any post-processing, pass the most selective randomness tests. The core of our extracting algorithm can be easily generalized for other physical processes

Source-Device-Independent Ultrafast Quantum Random Number Generation

Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers from the quadratures of an electromagnetic field without any assumption on the input state. The method allows us to eliminate the numbers that can be predicted due to the presence of classical and quantum side information. In particular, we introduce a procedure to estimate a bound on the conditional min-entropy based on the entropic uncertainty principle for position and momentum observables of infinite dimensional quantum systems. By the above method, we experimentally demonstrated the generation of secure true random bits at a rate greater than 1.7 Gbit/s

Loss tolerant device-independent quantum key distribution: a proof of principle

We here present the rate analysis and a proof of principle realization of a device-independent quantum key distribution (QKD) protocol requiring the lowest detection efficiency necessary to achieve a secure key compared to device-independent protocols known so far. The protocol is based on non-maximally entangled state and its experimental realization has been performed by two-photon bipartite entangled states. The improvement with respect to protocols involving maximally entangled states has been estimated.Comment: 8 pages, 4 figure + appendi

Extremal Quantum Correlations: Experimental Study with Two-qubit States

We explore experimentally the space of two-qubit quantum correlated mixed states, including frontier ones as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for the high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations.Comment: 5 pages, 2 figure

Source-device-independent heterodyne-based quantum random number generator at 17 Gbps

For many applications, quantum random number generation should be fast and independent from assumptions on the apparatus. Here, the authors devise and implement an approach which assumes a trusted detector but not a trusted source, and allows random bit generations at ~17 Gbps using off-the-shelf components