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We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasi-periodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). At intermediate interactions, the system undergoes an insulator to superfluid transition upon increasing the disorder, while a further increase of disorder strength drives the superfluid to Bose glass phase transition. While we are not able to discern between the Mott insulator and the Bose glass at intermediate interactions, we study the transition between these two phases at larger interaction strength and, unlike what reported in arXiv:1110.3213v3 for random disorder, find no evidence of a Mott-glass-like behavior.

We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed., Comment: 5 pages, 5 figures

Hard-core dipolar bosons trapped in a parallel stack of N>=2 1D optical lattices (tubes) can develop several phases made of composites of particles from different tubes: superfluids, supercounterfluids and insulators as well as mixtures of those. Bosonization analysis shows that these phases are threshold-less with respect to the dipolar interaction, with the key "control knob" being filling factors in each tube, provided the inter-tube tunneling is suppressed. The effective ab-initio quantum Monte Carlo algorithm capturing these phases is introduced and some results are presented.

Wyner's elegant model of wiretap channel exploits noise in the communication channel to provide perfect secrecy against a computationally unlimited eavesdropper without requiring a shared key. We consider an adversarial model of wiretap channel proposed in [18,19] where the adversary is active: it selects a fraction $\rho_r$ of the transmitted codeword to eavesdrop and a fraction $\rho_w$ of the codeword to corrupt by "adding" adversarial error. It was shown that this model also captures network adversaries in the setting of 1-round Secure Message Transmission [8]. It was proved that secure communication (1-round) is possible if and only if $\rho_r + \rho_w <1$. In this paper we show that by allowing communicants to have access to a public discussion channel (authentic communication without secrecy) secure communication becomes possible even if $\rho_r + \rho_w >1$. We formalize the model of \awtppd protocol and for two efficiency measures, {\em information rate } and {\em message round complexity} derive tight bounds. We also construct a rate optimal protocol family with minimum number of message rounds. We show application of these results to Secure Message Transmission with Public Discussion (SMT-PD), and in particular show a new lower bound on transmission rate of these protocols together with a new construction of an optimal SMT-PD protocol.

In [13] we proposed a ({\rho}_r , {\rho}_w )-adversarial wiretap channel model (AWTP) in which the adversary can adaptively choose to see a fraction {\rho}_r of the codeword sent over the channel, and modify a fraction {\rho}_w of the codeword by adding arbitrary noise values to them. In this paper we give the first efficient construction of a capacity achieving code family that provides perfect secrecy for this channel.

Sending private messages over communication environments under surveillance is an important challenge in communication security and has attracted attentions of cryptographers through time. We believe that resources other than cryptographic keys can be used for communication privacy. We consider private message transmission (PMT) in an abstract multipath communication model between two communicants, Alice and Bob, in the presence of an eavesdropper, Eve. Alice and Bob have pre-shared keys and Eve is computationally unbounded. There are a total of $n$ paths and the three parties can have simultaneous access to at most $t_a$, $t_b$, and $t_e$ paths. The parties can switch their paths after every $\lambda$ bits of communication. We study perfect (P)-PMT versus asymptotically-perfect (AP)-PMT protocols. The former has zero tolerance of transmission error and leakage, whereas the latter allows for positive error and leakage that tend to zero as the message length increases. We derive the necessary and sufficient conditions under which P-PMT and AP-PMT are possible. We also introduce explicit P-PMT and AP-PMT constructions. Our results show AP-PMT protocols attain much higher information rates than P-PMT ones. Interestingly, AP-PMT is possible even in poorest condition where $t_a=t_b=1$ and $t_e=n-1$. It remains however an open question whether the derived rates can be improved by more sophisticated AP-PMT protocols. We study applications of our results to private communication over the real-life scenarios of multiple-frequency links and multiple-route networks. We show practical examples of such scenarios that can be abstracted by the multipath setting: Our results prove the possibility of keyless information-theoretic private message transmission at rates $17\%$ and $20\%$ for the two example scenarios, respectively. We discuss open problems and future work at the end.

In wiretap model of secure communication the goal is to provide (asymptotic) perfect secrecy and reliable communication over a noisy channel that is eavesdropped by an adversary with unlimited computational power. This goal is achieved by taking advantage of the channel noise and without requiring a shared key. The model has attracted attention in recent years because it captures eavesdropping attack in wireless communication. The wiretap adversary is a passive eavesdropping adversary at the physical layer of communication. In this paper we propose a model for adversarial wiretap (AWTP) channel that models active adversaries at this layer. We consider a $(\rho_r, \rho_w)$ wiretap adversary who can see a fraction $\rho_r$, and modify a fraction $\rho_w$, of the sent codeword. The code components that are read and/or modified can be chosen adaptively, and the subsets of read and modified components in general, can be different. AWTP codes provide secrecy and reliability for communication over these channels. We give security and reliability definitions and measures for these codes, and define secrecy capacity of an AWTP channel that represents the secrecy potential of the channel. The paper has two main contributions. First, we prove a tight upper bound on the rate of AWTP codes with perfect secrecy for $(\rho_r, \rho_w)$-AWTP channels, and use the bound to derive the secrecy capacity of the channel. We prove a similar bound for $\epsilon$-secure codes also, but in this case the bound is not tight. Second, we give an explicit construction for a capacity achieving AWTP code family, and prove its security and efficiency properties. We show that AWTP model is a natural generalization of Wyner's wiretap models and somewhat surprisingly, also provides a direct generalization for a seemingly unrelated cryptographic primitive, Secure Message Transmission (SMT).

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}., Comment: 23 pages, A preliminary version appears in the 12th International Conference on Cryptology and Network Security (CANS 2013)

We introduce randomized Limited View (LV) adversary codes that provide protection against an adversary that uses their partial view of the communication to construct an adversarial error vector to be added to the channel. For a codeword of length N, the adversary selects a subset of \rho_rN of the codeword components to "see", and then "adds" an adversarial error vector of weight \rho_wN to the codeword. Performance of the code is measured by the probability of the decoder failure in recovering the sent message. An (N, q^{RN},\delta)-limited view adversary code ensures that the success chance of the adversary in making decoder fail, is bounded by \delta when the information rate of the code is at least R. Our main motivation to study these codes is providing protection for wireless communication at the physical layer of networks. We formalize the definition of adversarial error and decoder failure, construct a code with efficient encoding and decoding that allows the adversary to, depending on the code rate, read up to half of the sent codeword and add error on the same coordinates. The code is non-linear, has an efficient decoding algorithm, and is constructed using a message authentication code (MAC) and a Folded Reed-Solomon (FRS) code. The decoding algorithm uses an innovative approach that combines the list decoding algorithm of the FRS codes and the MAC verification algorithm to eliminate the exponential size of the list output from the decoding algorithm. We discuss application of our results to Reliable Message Transmission problem, and open problems for future work.

We consider the problem of distance bounding verification (DBV), where a proving party claims a distance and a verifying party ensures that the prover is within the claimed distance. Current approaches to "secure" distance estimation use signal's time of flight, which requires the verifier to have an accurate clock. We study secure DBV using physical channel properties as an alternative to time measurement. We consider a signal propagation environment that attenuates signal as a function of distance, and then corrupts it by an additive noise. We consider three attacking scenarios against DBV, namely distance fraud (DFA), mafia fraud (MFA) and terrorist fraud (TFA) attacks. We show it is possible to construct efficient DBV protocols with DFA and MFA security, even against an unbounded adversary; on the other hand, it is impossible to design TFA-secure protocols without time measurement, even with a computationally-bounded adversary. We however provide a TFA-secure construction under the condition that the adversary's communication capability is limited to the bounded retrieval model (BRM). We use numerical analysis to examine the communication complexity of the introduced DBV protocols. We discuss our results and give directions for future research.

We study the behavior of the bound state energy of a system consisting of two identical heavy fermions of mass M and a light particle of mass m. The heavy fermions interact with the light particle through a short-range two-body potential with positive s-wave scattering length a_s. We impose a short-range boundary condition on the logarithmic derivative of the hyperradial wavefunction and show that, in the regime where Efimov states are absent, a non-universal three-body state "cuts through" the universal three-body states previously described by Kartavtsev and Malykh [O. I. Kartavtsev and A. V. Malykh, J. Phys. B 40, 1429 (2007)]. The presence of the non-universal state alters the behavior of the universal states in certain regions of the parameter space. We show that the existence of the non-universal state is predicted accurately by a simple quantum defect theory model that utilizes hyperspherical coordinates. An empirical two-state model is employed to quantify the coupling of the non-universal state to the universal states., Comment: 7 pages, 7 figures

Electric field noise is a hinderance to the assembly of large scale quantum computers based on entangled trapped ions. Apart from ubiquitous technical noise sources, experimental studies of trapped ion heating have revealed additional limiting contributions to this noise, originating from atomic processes on the electrode surfaces. In a recent work [A. Safavi-Naini et al., Phys. Rev. A 84, 023412 (2011)] we described a microscopic model for this excess electric field noise, which points a way towards a more systematic understanding of surface adsorbates as progenitors of electric field jitter noise. Here, we address the impact of surface monolayer contamination on adsorbate induced noise processes. By using exact numerical calculations for H and N atomic monolayers on an Au(111) surface representing opposite extremes of physisorption and chemisorption, we show that an additional monolayer can significantly affect the noise power spectrum and either enhance or suppress the resulting heating rates., Comment: 8 pages, 5 figures

We investigate the quantum phases of hard-core dipolar bosons confined to a square lattice in a bilayer geometry. Using exact theoretical techniques, we discuss the many-body effects resulting from pairing of particles across layers at finite density, including a novel pair supersolid phase, superfluid and solid phases. These results are of direct relevance to experiments with polar molecules and atoms with large magnetic dipole moments trapped in optical lattices., Comment: 7 pages, 5 figures

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for sufficiently attractive three-body interaction the n = 2 Mott lobe disappears and the system displays first order phase transitions separating the n = 1 from the n = 3 lobes, and the n = 1 and n = 3 Mott insulator from the superfluid. We have also analyzed the effect of finite temperature and found that transitions are still of first order at temperatures T\simJ where J is the hopping matrix element., Comment: introduction slightly changed, modified figures

Motional heating of ions in micro-fabricated traps is a challenge hindering experimental realization of large-scale quantum processing devices. Recently a series of measurements of the heating rates in surface-electrode ion traps characterized their frequency, distance, and temperature dependencies, but our understanding of the microscopic origin of this noise is still vague. In this work we develop a theoretical model for the electric field noise which is associated with a random distribution of adsorbed atoms on the trap electrode surface. By using first principle calculations of the fluctuating dipole moments of the adsorbed atoms we evaluate the distance, frequency and temperature dependence of the resulting electric field fluctuation spectrum.Our theory calculates the noise spectrum beyond the standard scenario of two-level fluctuators, by incorporating all the relevant vibrational states. The $1/f$ noise is shown to commence at roughly the frequency of the fundamental phonon transition rate and the $d^{-4}$ dependence with distance of the ion from the electrode surface is established., Comment: 8 pages, 7 figures, updated to match PRA version