Weak Zero-Knowledge Beyond the Black-Box Barrier

The round complexity of zero-knowledge protocols is a long-standing open question, yet to be settled under standard assumptions. So far, the question has appeared equally challenging for relaxations such as weak zero-knowledge and witness hiding. Protocols satisfying these relaxed notions under standard assumptions have at least four messages, just like full-fledged zero knowledge. The difficulty in improving round complexity stems from a fundamental barrier: none of these notions can be achieved in three messages via reductions (or simulators) that treat the verifier as a black box. We introduce a new non-black-box technique and use it to obtain the first protocols that cross this barrier under standard assumptions. Our main results are: \begin{itemize} \item Weak zero-knowledge for $NP$in two messages, assuming quasipolynomially-secure fully-homomorphic encryption and other standard primitives (known from quasipolynomial hardness of Learning with Errors), as well as subexponentially-secure one-way functions. \item Weak zero-knowledge for $NP$ in three messages under standard polynomial assumptions (following for example from fully-homomorphic encryption and factoring). \end{itemize} We also give, under polynomial assumptions, a two-message witness-hiding protocol for any language $L \in NP$ that has a witness encryption scheme. This protocol is also publicly verifiable. Our technique is based on a new {\em homomorphic trapdoor paradigm}, which can be seen as a non-black-box analog of the classic Feige-Lapidot-Shamir trapdoor paradigm

Non-Black-Box Approach to Secure Two-Party Computation in Three Rounds

The round complexity of secure two-party computation is a long studied problem with matching upper and lower bounds for the case of black-box simulators (i.e., the simulators that use the adversary as a black-box). In this work, we focus on going beyond this black-box barrier via non-black-box techniques. Specifically, based on standard cryptographic assumptions, we give a construction of a 3-round two-party computation protocol for computing inputless functionalities (such as coin-tossing) that satisfies standard security against malicious senders and $\epsilon$-security against malicious receivers. Prior to our work such protocols were only known for the case of (weak) zero-knowledge

Wetting hysteresis induced by nanodefects

Wetting of actual surfaces involves diverse hysteretic phenomena stemming from ever-present imperfections. Here, we clarify the origin of wetting hysteresis for a liquid front advancing or receding across an isolated defect of nanometric size. Various kinds of chemical and topographical nanodefects, which represent salient features of actual heterogeneous surfaces, are investigated. The most probable wetting path across surface heterogeneities is identified by combining, within an innovative approach, microscopic classical density functional theory and the string method devised for the study of rare events. The computed rugged free-energy landscape demonstrates that hysteresis emerges as a consequence of metastable pinning of the liquid front at the defects; the barriers for thermally activated defect crossing, the pinning force, and hysteresis are quantified and related to the geometry and chemistry of the defects allowing for the occurrence of nanoscopic effects. The main result of our calculations is that even weak nanoscale defects, which are difficult to characterize in generic microfluidic experiments, can be the source of a plethora of hysteretical phenomena, including the pinning of nanobubbles

Many-body processes in black and grey matter-wave solitons

We perform a comparative beyond mean-field study of black and grey solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized density-engineering potential is developed and employed together with phase-imprinting to cleanly initialize grey solitons. Based on our recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons, we demonstrate an enhancement of the quantum fluctuations limited lifetime of the soliton contrast with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of grey solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analysed in detail. Finally, the role of phase-imprinting for the many-body dynamics is illuminated and additional non-local correlations in pairs of counter-propagating grey solitons are unravelled

Self-Completeness of Einstein Gravity

We argue, that in Einsteinian gravity the Planck length is the shortest length of nature, and any attempt of resolving trans-Planckian physics bounces back to macroscopic distances due to black hole formation. In Einstein gravity trans-Planckian propagating quantum degrees of freedom cannot exist, instead they are equivalent to the classical black holes that are fully described by lighter infra-red degrees of freedom and give exponentially-soft contribution into the virtual processes. Based on this property we argue that pure-Einstein (super)gravity and its high-dimensional generalizations are self-complete in deep-UV, but not in standard Wilsonian sense. We suggest that certain strong-coupling limit of string theory is built-in in pure Einstein gravity, whereas the role of weakly-coupled string theory limit is to consistently couple gravity to other particle species, with their number being set by the inverse string coupling. We also discuss some speculative ideas generalizing the notion of non-Wilsonian self-completeness to other theories, such as the standard model without the Higgs.Comment: 40 pages, Late

Characteristic molecular properties of one-electron double quantum rings under magnetic fields

The molecular states of conduction electrons in laterally coupled quantum rings are investigated theoretically. The states are shown to have a distinct magnetic field dependence, which gives rise to periodic fluctuations of the tunnel splitting and ring angular momentum in the vicinity of the ground state crossings. The origin of these effects can be traced back to the Aharonov-Bohm oscillations of the energy levels, along with the quantum mechanical tunneling between the rings. We propose a setup using double quantum rings which shows that Aharonov-Bohm effects can be observed even if the net magnetic flux trapped by the carriers is zero.Comment: 16 pages (iopart format), 10 figures, accepted in J.Phys.Cond.Mat

Impurity effects on semiconductor quantum bits in coupled quantum dots

We theoretically consider the effects of having unintentional charged impurities in laterally coupled two-dimensional double (GaAs) quantum dot systems, where each dot contains one or two electrons and a single charged impurity in the presence of an external magnetic field. Using molecular orbital and configuration interaction method, we calculate the effect of the impurity on the 2-electron energy spectrum of each individual dot as well as on the spectrum of the coupled-double-dot 2-electron system. We find that the singlet-triplet exchange splitting between the two lowest energy states, both for the individual dots and the coupled dot system, depends sensitively on the location of the impurity and its coupling strength (i.e. the effective charge). A strong electron-impurity coupling breaks down equality of the two doubly-occupied singlets in the left and the right dot leading to a mixing between different spin singlets. As a result, the maximally entangled qubit states are no longer fully obtained in zero magnetic field case. Moreover, a repulsive impurity results in a triplet-singlet transition as the impurity effective charge increases or/and the impurity position changes. We comment on the impurity effect in spin qubit operations in the double dot system based on our numerical results.Comment: published version on Physical Review B journal, 25 pages, 26 figure

Quantum Gravity Constraints on Inflation

We study quantum gravity constraints on inflationary model building. Our approach is based on requiring the entropy associated to a given inflationary model to be less than that of the de Sitter entropy. We give two prescriptions for determining the inflationary entropy, based on either `bits per unit area' or entanglement entropy. The existence of transPlanckian flat directions, necessary for large tensor modes in the CMB, correlates with an inflationary entropy greater than that allowed by de Sitter space. Independently these techniques also constrain or exclude de Sitter models with large-rank gauge groups and high UV cutoffs, such as racetrack inflation or the KKLT construction.Comment: 22 pages; v2 references adde