Monogamy of nonlocal quantum correlations

We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling probability distributions. This maximization can be cast as a linear program. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the trade-off between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.Comment: This is the submitted version. The refereed version, which contains an additional result about strong parallel repetition and corrects some typos, is available on my personal web site at http://bentoner.com/papers/monogamyrs.pdf [PDF

Polynomial Bounds On Parallel Repetition For All 3-Player Games With Binary Inputs

We prove that for every 3-player (3-prover) game $\mathcal G$ with value less than one, whose query distribution has the support $\mathcal S = \{(1,0,0), (0,1,0), (0,0,1)\}$ of hamming weight one vectors, the value of the $n$-fold parallel repetition $\mathcal G^{\otimes n}$ decays polynomially fast to zero; that is, there is a constant $c = c(\mathcal G)>0$ such that the value of the game $\mathcal G^{\otimes n}$ is at most $n^{-c}$. Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC 2022), our result is the missing piece that implies a similar bound for a much more general class of multiplayer games: For $\textbf{every}$ 3-player game $\mathcal G$ over $\textit{binary questions}$ and $\textit{arbitrary answer lengths}$, with value less than 1, there is a constant $c = c(\mathcal G)>0$ such that the value of the game $\mathcal G^{\otimes n}$ is at most $n^{-c}$. Our proof technique is new and requires many new ideas. For example, we make use of the Level-$k$ inequalities from Boolean Fourier Analysis, which, to the best of our knowledge, have not been explored in this context prior to our work

Instabilities in a Liquid-Fluidized Bed of Gas Bubbles

Gas bubbles in an aqueous foam can be unjammed, or fluidized, by introducing a forced flow of the continuous liquid phase at a sufficiently high rate. We observe that the resulting bubble dynamics are spatially inhomogeneous, exhibiting a sequence of instabilities vs increasing flow rate. First irregular swirls appear, then a single convective roll, and finally a series of stratified convection rolls each with a different average bubble size

Time-Resolved Measurements of Shock-Compressed Matter using X-rays.

Thermonuclear fusion occurs at extremely high pressures and densities. Producing thermonuclear fusion in the laboratory requires a detailed understanding of material properties beyond the scope of condensed matter or classical plasma physics, requiring experimental data to improve models describing matter in these extreme states. This thesis reports the development of two improved methods to probe highly compressed matter using x-ray diagnostics. The first method uses time-resolved x-ray diffraction to infer the stresses in compressed polycrystalline materials. X-ray diffraction is capable of measuring strain states and densities in shock-compressed materials with significantly higher accurately than existing shock timing and velocimetry diagnostics. The analysis discussed in this thesis calculates Debye-Scherrer diffraction patterns from highly stressed polycrystalline samples in the Reuss (iso-stress) limit. In this limit, elastic anisotropy and sample texture effects are directly modeled using elastic constants to calculate lattice strains for all initial crystallite orientations. Example diffraction patterns showing the effects of probing geometry, deviatoric stresses, and sample texture are presented to highlight the versatility of the technique. Finally, I present the design of a recent experiment conducted at the Linac Coherent Light Source to measure the strength of polycrystalline diamond whose data can be analyzed using this technique. The second method uses x-ray fluorescence (XRF) to measure density, ionization state populations, and electron temperature in shocked materials. Spatially resolved K-alpha intensity measurements enable measurements of ion density profiles. Ionization state distributions and electron temperatures are constrained by comparing K-alpha spectra to spectra from atomic-physics simulations using the computer code CRETIN. Analysis of experimental data from the Trident laser facility measuring Ti K-alpha emission spectra from shock-compressed foams demonstrates the use of the technique. This work shows that XRF spectroscopy is a useful technique to complement prior diagnostics to make equation of state measurements of shocked materials containing a suitable tracer element.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135774/1/macdonm_1.pd

An Improved Foam Modeling Technique and Its Application to Petroleum Drilling and Production Practice

Foam is one of the most common used multiphase fluid in Underbalanced Drilling (UBD) and Managed Pressure Drilling (MPD). Because of its low density, high capacity of lifting and carrying cuttings, low cost and compatibility with formations, foam has become more superior than the conventional drilling mud when depleted reservoir pressure, severe lost circulation, or unstable borehole are encountered. In general, the success of foam applications rely on the understanding of the fundamentals of foam rheology in downhole conditions. Foam rheology has been studied for decades. Conventional foam rheological models such as Power Law, Bingham Plastic, Herschel-Bulkley to explain foam behavior usually fail to interpret the monitored circulating pressure changes in operation, not to mention foam behaviors in downhole. Understanding bubble size and foam texture impacts at different foam quality ranges in the foam model development become very significant. A new foam rheological model based on Low-Quality Regime (LQR) and High-Quality Regime (HQR) behaviors is developed. This new model, which originally came from comprehensive foam flow experiments, together with the visualization of foam texture and bubble distribution, is proved to be easily and conveniently implemented for industry use in this study. The model requires nine model parameters – three (uwRef, ugRef,DPRef) to define the transition region, four to capture Power-Law rheology in both HQR and LQR (KH, nH, KL, nL), and two to describe the sensitivity of steady-state pressure drops as a function of gas and liquid velocities in both regimes (mH, mL). With the newly developed foam model, we apply it in the following two foam applications in petroleum industry, in which the foam rheology and foam handling are the main concerns for successes. First of all, a foam drilling and wellbore clean-up application with foam is investigated. These scenarios consider foam circulation into 10000 ft long wells at different inclination angles with a long vertical, inclined, or horizontal trajectory. The results are compared with two existing foam modeling techniques, so-called Chen et al.’s model (based on the correlations for wet foams only) and Edrisi and Kam’s model (based on wet- and dry-foam rheological properties with five model parameters). The conclusions show that, with or without formation fluid influx, the new foam model demonstrates the robustness of the new modeling technique in all scenarios capturing foam flow characteristics better, whenever the situation forms stable fine-textured foams or unstable coarse-textured foams. Second, foam-assisted mud cap drilling for gas migration situation, which simulatesthe process with accurate foam characteristics when foams are used to suppress gas kicks under certain well and fluid conditions, is presented. The new foam model with Two Flow Regimes is used throughout the simulation process. The results show how mud-cap drilling parameters (such as pressure, foam density (or equivalent mud weight), foam velocity, and foam quality) change at different operating conditions and scenarios. Moreover, a set of field data from a wellbore clean-up with foam operation is demonstrated and the circulating pressure changes provide the evidence of Two Flow Regimes

Polynomial Bounds on Parallel Repetition for All 3-Player Games with Binary Inputs

We prove that for every 3-player (3-prover) game G with value less than one, whose query distribution has the support S = {(1,0,0), (0,1,0), (0,0,1)} of Hamming weight one vectors, the value of the n-fold parallel repetition G^{?n} decays polynomially fast to zero; that is, there is a constant c = c(G) > 0 such that the value of the game G^{?n} is at most n^{-c}. Following the recent work of Girish, Holmgren, Mittal, Raz and Zhan (STOC 2022), our result is the missing piece that implies a similar bound for a much more general class of multiplayer games: For every 3-player game G over binary questions and arbitrary answer lengths, with value less than 1, there is a constant c = c(G) > 0 such that the value of the game G^{?n} is at most n^{-c}. Our proof technique is new and requires many new ideas. For example, we make use of the Level-k inequalities from Boolean Fourier Analysis, which, to the best of our knowledge, have not been explored in this context prior to our work