AirCode: Unobtrusive Physical Tags for Digital Fabrication

We present AirCode, a technique that allows the user to tag physically fabricated objects with given information. An AirCode tag consists of a group of carefully designed air pockets placed beneath the object surface. These air pockets are easily produced during the fabrication process of the object, without any additional material or postprocessing. Meanwhile, the air pockets affect only the scattering light transport under the surface, and thus are hard to notice to our naked eyes. But, by using a computational imaging method, the tags become detectable. We present a tool that automates the design of air pockets for the user to encode information. AirCode system also allows the user to retrieve the information from captured images via a robust decoding algorithm. We demonstrate our tagging technique with applications for metadata embedding, robotic grasping, as well as conveying object affordances.Comment: ACM UIST 2017 Technical Paper

Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes

Efficient multi-point local decoding of Reed-Muller codes via interleaved codex

Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple coordinates simultaneously, the naive way is to repeat the local decoding for recovery of a single coordinate. This decoding algorithm might be more expensive, i.e., require higher query complexity. In this paper, we focus on Reed-Muller codes with usual parameter regime, namely, the total degree of evaluation polynomials is d=Θ {q), where q is the code alphabet size (in fact, d can be as big as q/4 in our setting). By introducing a novel variation of codex, i.e., interleaved codex (the concept of codex has been used for arithmetic secret sharing), we are able to locally recover arbitrarily large number k of coordinates of a Reed-Muller code simultaneously with error probability exp (-Ω (k)) at the cost of querying merely O(q2k) coordinates. It turns out that our local decoding of Reed-Muller codes shows (perhaps surprisingly) that accessing k locations is in fact cheaper than repeating the procedure for accessing a single location for k times. Precisely speaking, to get the same success probability by repeating the local decoding algorithm of a single coordinate, one has to query Ω (qk2) coordinates. Thus, the query complexity of our local decoding is smaller for k=Ω (q). If we impose the same query complexity constraint on both algorithm, our local decoding algorithm yields smaller error probability when k=Ω (qq). In addition, our local decoding is efficient, i.e., the decoding complexity is Poly(k,q). Construction of an interleaved codex is based on concatenation of a codex with a multiplication friendly pair, while the main tool to realize codex is based on algebraic function fields (or more precisely, algebraic geometry codes)

Quantum Private Information Retrieval from Coded Storage Systems

In the era of extensive data growth, robust and efficient mechanisms are needed to store and manage vast amounts of digital information, such as Data Storage Systems (DSSs). Concurrently, privacy concerns have arisen, leading to the development of techniques like Private Information Retrieval (PIR) to enable data access while preserving privacy. A PIR protocol allows users to retrieve information from a database without revealing the specifics of their query or the data they are accessing. With the advent of quantum computing, researchers have explored the potential of using quantum systems to enhance privacy in information retrieval. In a Quantum Private Information Retrieval (QPIR) protocol, a user can retrieve information from a database by downloading quantum systems from multiple servers, while ensuring that the servers remain oblivious to the specific information being accessed. This scenario offers a unique advantage by leveraging the inherent properties of quantum systems to provide enhanced privacy guarantees and improved communication rates compared to classical PIR protocols. In this thesis we consider the QPIR setting where the queries and the coded storage systems are classical, while the responses from the servers are quantum. This problem was treated by Song et al. for replicated storage and different collusion patterns. This thesis aims to develop QPIR protocols for coded storage by combining known classical PIR protocols with quantum communication algorithms, achieving enhanced privacy and communication costs. We consider different storage codes and robustness assumptions, and we prove that the achieved communication cost is always lower than the classical counterparts.Comment: This is the summary part of an article collection-based PhD thesi

Inverse-design of high-dimensional quantum optical circuits in a complex medium

Programmable optical circuits form a key part of quantum technologies today, ranging from transceivers for quantum communication to integrated photonic chips for quantum information processing. As the size of such circuits is increased, maintaining precise control over every individual component becomes challenging, leading to a reduction in the quality of the operations performed. In parallel, minor imperfections in circuit fabrication are amplified in this regime, dramatically inhibiting their performance. Here we show how embedding an optical circuit in the higher-dimensional space of a large, ambient mode-mixer using inverse-design techniques allows us to forgo control over each individual circuit element, while retaining a high degree of programmability over the circuit. Using this approach, we implement high-dimensional linear optical circuits within a complex scattering medium consisting of a commercial multi-mode fibre placed between two controllable phase planes. We employ these circuits to manipulate high-dimensional spatial-mode entanglement in up to seven dimensions, demonstrating their application as fully programmable quantum gates. Furthermore, we show how their programmability allows us to turn the multi-mode fibre itself into a generalised multi-outcome measurement device, allowing us to both transport and certify entanglement within the transmission channel. Finally, we discuss the scalability of our approach, numerically showing how a high circuit fidelity can be achieved with a low circuit depth by harnessing the resource of a high-dimensional mode-mixer. Our work serves as an alternative yet powerful approach for realising precise control over high-dimensional quantum states of light, with clear applications in next-generation quantum communication and computing technologies

Greedy weights for matroids

We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we show that in the cases where the matroids involved are associated to linear codes, our definitions coincide with those for codes. Thus our Wei duality is a generalization of that for linear codes given by Schaathun. In the last part of the paper we show how some important chains of cycles of the matroids appearing, correspond to chains of component maps of minimal resolutions of the independence complex of the corresponding matroids. We also relate properties of these resolutions to chainedness and greedy weights of the matroids, and in many cases codes, that appear.Comment: 17 page

Automated color correction for colorimetric applications using barcodes

[eng] Color-based sensor devices often offer qualitative solutions, where a material change its color from one color to another, and this is change is observed by a user who performs a manual reading. These materials change their color in response to changes in a certain physical or chemical magnitude. Nowadays, we can find colorimetric indicators with several sensing targets, such as: temperature, humidity, environmental gases, etc. The common approach to quantize these sensors is to place ad hoc electronic components, e.g., a reader device. With the rise of smartphone technology, the possibility to automatically acquire a digital image of those sensors and then compute a quantitative measure is near. By leveraging this measuring process to the smartphones, we avoid the use of ad hoc electronic components, thus reducing colorimetric application cost. However, there exists a challenge on how-to acquire the images of the colorimetric applications and how-to do it consistently, with the disparity of external factors affecting the measure, such as ambient light conditions or different camera modules. In this thesis, we tackle the challenges to digitize and quantize colorimetric applications, such as colorimetric indicators. We make a statement to use 2D barcodes, well-known computer vision patterns, as the base technology to overcome those challenges. We focus on four main challenges: (I) to capture barcodes on top of real-world challenging surfaces (bottles, food packages, etc.), which are the usual surface where colorimetric indicators are placed; (II) to define a new 2D barcode to embed colorimetric features in a back-compatible fashion; (III) to achieve image consistency when capturing images with smartphones by reviewing existent methods and proposing a new color correction method, based upon thin-plate splines mappings; and (IV) to demonstrate a specific application use case applied to a colorimetric indicator for sensing CO2 in the range of modified atmosphere packaging, MAP, one of the common food-packaging standards.[cat] Els dispositius de sensat basats en color, normalment ofereixen solucions qualitatives, en aquestes solucions un material canvia el seu color a un altre color, i aquest canvi de color és observat per un usuari que fa una mesura manual. Aquests materials canvien de color en resposta a un canvi en una magnitud física o química. Avui en dia, podem trobar indicadors colorimètrics que amb diferents objectius, per exemple: temperatura, humitat, gasos ambientals, etc. L'opció més comuna per quantitzar aquests sensors és l'ús d'electrònica addicional, és a dir, un lector. Amb l'augment de la tecnologia dels telèfons intel·ligents, la possibilitat d'automatitzar l'adquisició d'imatges digitals d'aquests sensors i després computar una mesura quantitativa és a prop. Desplaçant aquest procés de mesura als telèfons mòbils, evitem l'ús d'aquesta electrònica addicional, i així, es redueix el cost de l'aplicació colorimètrica. Tanmateix, existeixen reptes sobre com adquirir les imatges de les aplicacions colorimètriques i de com fer-ho de forma consistent, a causa de la disparitat de factors externs que afecten la mesura, com per exemple la llum ambient or les diferents càmeres utilitzades. En aquesta tesi, encarem els reptes de digitalitzar i quantitzar aplicacions colorimètriques, com els indicadors colorimètrics. Fem una proposició per utilitzar codis de barres en dues dimensions, que són coneguts patrons de visió per computador, com a base de la nostra tecnologia per superar aquests reptes. Ens focalitzem en quatre reptes principals: (I) capturar codis de barres sobre de superfícies del món real (ampolles, safates de menjar, etc.), que són les superfícies on usualment aquests indicadors colorimètrics estan situats; (II) definir un nou codi de barres en dues dimensions per encastar elements colorimètrics de forma retro-compatible; (III) aconseguir consistència en la captura d'imatges quan es capturen amb telèfons mòbils, revisant mètodes de correcció de color existents i proposant un nou mètode basat en transformacions geomètriques que utilitzen splines; i (IV) demostrar l'ús de la tecnologia en un cas específic aplicat a un indicador colorimètric per detectar CO2 en el rang per envasos amb atmosfera modificada, MAP, un dels estàndards en envasos de menjar.