Experimental nonlinear sign shift for linear optics quantum computation

We have realized the nonlinear sign shift (NS) operation for photonic qubits.This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift is $(1.05\pm 0.06) \pi$ in clear agreement with theory. Our results show that by using an ancilla photon and conditional detection, nonlinear optical effects can be implemented using only linear optical elements. This experiment represents an essential step for linear optical implementations of scalable quantum computation.Comment: 4 pages, 4 figure

Feed-in Tariffs and Quotas for Renewable Energy in Europe

Regenerative Energie, Elektrizität, Stromtarif, Förderung regenerativer Energien, EU-Staaten, Renewable energy, Electricity, Electricity price, Renewable energy policy, EU countries

Observation of genuine three-photon interference

Multiparticle quantum interference is critical for our understanding and exploitation of quantum information, and for fundamental tests of quantum mechanics. A remarkable example of multi-partite correlations is exhibited by the Greenberger-Horne-Zeilinger (GHZ) state. In a GHZ state, three particles are correlated while no pairwise correlation is found. The manifestation of these strong correlations in an interferometric setting has been studied theoretically since 1990 but no three-photon GHZ interferometer has been realized experimentally. Here we demonstrate three-photon interference that does not originate from two-photon or single photon interference. We observe phase-dependent variation of three-photon coincidences with 90.5 \pm 5.0 % visibility in a generalized Franson interferometer using energy-time entangled photon triplets. The demonstration of these strong correlations in an interferometric setting provides new avenues for multiphoton interferometry, fundamental tests of quantum mechanics and quantum information applications in higher dimensions.Comment: 7 pages, 7 figure

Chromate Adsorption on Amorphous Iron Oxyhydroxide in the Presence of Major Groundwater Ions

Chromate adsorption on amorphous iron oxyhydroxide was investigated in dilute iron suspensions as a single solute and in solutions of increasing complexity containing CO2 (g), SO42-(aq), H4Si04(aq), and cations [K+, Mg2+, Ca2+(aq)]. In paired-solute systems (e.g., CrO42- =H2CO3*), anionic cosolutes markedly reduce CrO42- adsorption through a combination of competitive and electrostatic effects, but cations exert no appreciable influence. Additionally, H4Si04 exhibits a strong time-dependent effect: CrO42- adsorption is greatly decreased with increasing H4SiO4 contact time. In multiple-ion mixtures, each anion added to the mixture decreases CrO42- adsorption further. Adsorption constants for the individual reactive solutes were used in the triple-layer model. The model calculations are in good agreement with the CrO42- adsorption data for paired- and multiple-solute systems. However, the model calculations underestimate CrO42- adsorption when surface site saturation is appr6ached. Questions remain regarding the surface interactions of both CO2(aq) and H4Si04. The results have major implications for the adsorption behavior of CrO42- and other oxyanions in subsurface waters

The Virtual Acoustic Spaces Unity Spatializer with custom head tracker

The virtual acoustic spaces (VAS) unity spatializer is a plugin for dynamic binaural synthesis for Unity. It can handle impulse responses (IRs) of arbitrary length (limited only by hardware resources). Hence, it is possible to calculate the binaural synthesis not only with head related transfer functions (HRTFs), but also on the basis of binaural room impulse responses (BRIRs). The plugin can also virtualize reflections calculated by raytracing and it is possible to load an individual IR set for each instance. In addition to being compatible with off-the-shelf cross reality (XR) hardware it features a Bluetooth binding for an easily built, custom-made head tracker based on an ESP32 board. It is therefore predestined for audio augmented reality applications

Worst and Average Case Hardness of Decoding via Smoothing Bounds

In this work, we consider the worst and average case hardness of the decoding problems that are the basis for code-based cryptography. By a decoding problem, we consider inputs of the form $(\mathbf{G}, \mathbf{m} \mathbf{G} + \mathbf{t})$ for a matrix $\mathbf{G}$ that generates a code and a noise vector $\mathbf{t}$, and the algorithm\u27s goal is to recover $\mathbf{m}$. We consider a natural strategy for creating a reduction to an average-case problem: from our input we simulate a Learning Parity with Noise (LPN) oracle, where we recall that LPN is essentially an average-case decoding problem where there is no a priori lower bound on the rate of the code. More formally, the oracle $\mathcal{O}_{\mathbf{x}}$ outputs independent samples of the form $\langle \mathbf{x}, \mathbf{a} \rangle + e$, where $\mathbf{a}$ is a uniformly random vector and $e$ is a noise bit. Such an approach is (implicit in) the previous worst-case to average-case reductions for coding problems (Brakerski et al Eurocrypt 2019, Yu and Zhang CRYPTO 2021). To analyze the effectiveness of this reduction, we use a smoothing bound derived recently by (Debris-Alazard et al IACR Eprint 2022), which quantifies the simulation error of this reduction. It is worth noting that this latter work crucially use a bound, known as the second linear programming bounds, on the weight distribution of the code generated here by $\mathbf{G}$. Our approach, which is Fourier analytic in nature, applies to any smoothing distribution (so long as it is radial); for our purposes, the best choice appears to be Bernoulli (although for the analysis it is most effective to study the uniform distribution over a sphere, and subsequently translate the bound back to the Bernoulli distribution by applying a truncation trick). Our approach works naturally when reducing from a worst-case instance, as well as from an average-case instance. While we are unable to improve the parameters of the worst-case to average-case reductions of Brakerski et al or Yu and Zhang, we think that our work highlights two important points. Firstly, in analyzing the average-case to average-case reduction we run into inherent limitations of this reduction template. Essentially, it appears hopeless to reduce to an LPN instance for which the noise rate is more than inverse-polynomially biased away from uniform. We furthermore uncover a surprising weakness in the second linear programming bound: we observe that it is essentially useless for the regime of parameters where the rate of the code is inverse polynomial in the block-length. By highlighting these shortcomings, we hope to stimulate the development of new techniques for reductions between cryptographic decoding problems

A Generalized Special-Soundness Notion and its Knowledge Extractors

A classic result in the theory of interactive proofs shows that a special-sound $\Sigma$-protocol is automatically a proof of knowledge. This result is very useful to have, since the latter property is typically tricky to prove from scratch, while the former is often easy to argue---if it is satisfied. While classic $\Sigma$-protocols often are special-sound, this is unfortunately not the case for many recently proposed, highly efficient interactive proofs, at least not in this strict sense. Motivated by this, the original result was recently generalized to $k$-special sound $\Sigma$-protocols (for arbitrary, polynomially bounded $k$), and to multi-round versions thereof. This generalization is sufficient to analyze (e.g.) Bulletproofs-like protocols, but is still insufficient for many other examples. In this work, we push the relaxation of the special soundness property to the extreme, by allowing an arbitrary access structure $\Gamma$ to specify for which subsets of challenges it is possible to compute a witness, when given correct answers to these challenges (for a fixed first message). Concretely, for any access structure $\Gamma$, we identify parameters $t_\Gamma$ and $\kappa_\Gamma$, and we show that any $\Gamma$-special sound $\Sigma$-protocol is a proof of knowledge with knowledge error $\kappa_\Gamma$ if $t_\Gamma$ is polynomially bounded. Similarly for multi-round protocols. We apply our general result to a couple of simple but important example protocols, where we obtain a tight knowledge error as an immediate corollary. Beyond these simple examples, we analyze the FRI protocol. Here, showing the general special soundness notion is non-trivial, but can be done (for a certain range of parameters) by recycling some of the techniques used to argue ordinary soundness of the protocol (as an IOP). Again as a corollary, we then derive that the FRI protocol, as an interactive proof by using a Merkle-tree commitment, is a proof of knowledge with almost optimal knowledge error. Finally, building up on the technique for the parallel repetition of $k$-special sound $\Sigma$-protocols, we show the same strong parallel repetition result for $\Gamma$-special sound $\Sigma$-protocol and its multi-round variant