Quantum Proofs

Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum state plays the role of a proof (also called a certificate or witness), and is checked by a polynomial-time quantum computation. For some problems, the fact that a quantum proof state could be a superposition over exponentially many classical states appears to offer computational advantages over classical proof strings. In the interactive proof system setting, one may consider a verifier and one or more provers that exchange and process quantum information rather than classical information during an interaction for a given input string, giving rise to quantum complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit some properties from their classical counterparts, they also possess distinct and uniquely quantum features that lead to an interesting landscape of complexity classes based on variants of this model. In this survey we provide an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, we discuss non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class \class{QSZK}, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*.Comment: Survey published by NOW publisher

Quantum Key Distribution (QKD) and Commodity Security Protocols: Introduction and Integration

We present an overview of quantum key distribution (QKD), a secure key exchange method based on the quantum laws of physics rather than computational complexity. We also provide an overview of the two most widely used commodity security protocols, IPsec and TLS. Pursuing a key exchange model, we propose how QKD could be integrated into these security applications. For such a QKD integration we propose a support layer that provides a set of common QKD services between the QKD protocol and the security applicationsComment: 12Page

Tractability and the computational mind

We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effective algorithms is hardly possible. Some problems need too much computational resource, e.g., time or memory, to be practically computable. Computational complexity theory is concerned with the amount of resources required for the execution of algorithms and, hence, the inherent difficulty of computational problems. An important goal of computational complexity theory is to categorize computational problems via complexity classes, and in particular, to identify efficiently solvable problems and draw a line between tractability and intractability. We survey how complexity can be used to study computational plausibility of cognitive theories. We especially emphasize methodological and mathematical assumptions behind applying complexity theory in cognitive science. We pay special attention to the examples of applying logical and computational complexity toolbox in different domains of cognitive science. We focus mostly on theoretical and experimental research in psycholinguistics and social cognition

On Interference Cancellation and Iterative Techniques

Recent research activities in the area of mobile radio communications have moved to third generation (3G) cellular systems to achieve higher quality with variable transmission rate of multimedia information. In this paper, an overview is presented of various interference cancellation and iterative detection techniques that are believed to be suitable for 3G wireless communications systems. Key concepts are space-time processing and space-division multiple access (or SDMA) techniques. SDMA techniques are possible with software antennas. Furthermore, to reduce receiver implementation complexity, iterative detection techniques are considered. A particularly attractive method uses tentative hard decisions, made on the received positions with the highest reliability, according to some criterion, and can potentially yield an important reduction in the computational requirements of an iterative receiver, with minimum penalty in error performance. A study of the tradeoffs between complexity and performance loss of iterative multiuser detection techniques is a good research topic

Point Pair Feature based Object Detection for Random Bin Picking

Point pair features are a popular representation for free form 3D object detection and pose estimation. In this paper, their performance in an industrial random bin picking context is investigated. A new method to generate representative synthetic datasets is proposed. This allows to investigate the influence of a high degree of clutter and the presence of self similar features, which are typical to our application. We provide an overview of solutions proposed in literature and discuss their strengths and weaknesses. A simple heuristic method to drastically reduce the computational complexity is introduced, which results in improved robustness, speed and accuracy compared to the naive approach