Computing with Coloured Tangles

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams represent bisimilar computations. We prove that our model of computation is Turing complete, and that with bounded resources it can moreover decide any language in complexity class IP, sometimes with better performance parameters than corresponding classical protocols.Comment: 36 pages,; Introduction entirely rewritten, Section 4.3 adde

An Application of Quantum Finite Automata to Interactive Proof Systems

Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantum-automaton verifier through a common communication cell. Our quantum interactive proof systems are juxtaposed to Dwork-Stockmeyer's classical interactive proof systems whose verifiers are two-way probabilistic automata. We demonstrate strengths and weaknesses of our systems and further study how various restrictions on the behaviors of quantum-automaton verifiers affect the power of quantum interactive proof systems.Comment: This is an extended version of the conference paper in the Proceedings of the 9th International Conference on Implementation and Application of Automata, Lecture Notes in Computer Science, Springer-Verlag, Kingston, Canada, July 22-24, 200

A Game Theoretical Analysis of Localization Security in Wireless Sensor Networks with Adversaries

Wireless Sensor Networks (WSN) support data collection and distributed data processing by means of very small sensing devices that are easy to tamper and cloning: therefore classical security solutions based on access control and strong authentication are difficult to deploy. In this paper we look at the problem of assessing security of node localization. In particular, we analyze the scenario in which Verifiable Multilateration (VM) is used to localize nodes and a malicious node (i.e., the adversary) try to masquerade as non-malicious. We resort to non-cooperative game theory and we model this scenario as a two-player game. We analyze the optimal players' strategy and we show that the VM is indeed a proper mechanism to reduce fake positions.Comment: International Congress on Ultra Modern Telecommunications and Control Systems 2010. (ICUMT'10

Quantum money with nearly optimal error tolerance

We present a family of quantum money schemes with classical verification which display a number of benefits over previous proposals. Our schemes are based on hidden matching quantum retrieval games and they tolerate noise up to 23%, which we conjecture reaches 25% asymptotically as the dimension of the underlying hidden matching states is increased. Furthermore, we prove that 25% is the maximum tolerable noise for a wide class of quantum money schemes with classical verification, meaning our schemes are almost optimally noise tolerant. We use methods in semi-definite programming to prove security in a substantially different manner to previous proposals, leading to two main advantages: first, coin verification involves only a constant number of states (with respect to coin size), thereby allowing for smaller coins; second, the re-usability of coins within our scheme grows linearly with the size of the coin, which is known to be optimal. Lastly, we suggest methods by which the coins in our protocol could be implemented using weak coherent states and verified using existing experimental techniques, even in the presence of detector inefficiencies.Comment: 17 pages, 5 figure

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

Verifying Safety Properties With the TLA+ Proof System

TLAPS, the TLA+ proof system, is a platform for the development and mechanical verification of TLA+ proofs written in a declarative style requiring little background beyond elementary mathematics. The language supports hierarchical and non-linear proof construction and verification, and it is independent of any verification tool or strategy. A Proof Manager uses backend verifiers such as theorem provers, proof assistants, SMT solvers, and decision procedures to check TLA+ proofs. This paper documents the first public release of TLAPS, distributed with a BSD-like license. It handles almost all the non-temporal part of TLA+ as well as the temporal reasoning needed to prove standard safety properties, in particular invariance and step simulation, but not liveness properties