Multiple‐systems analysis for the quantification of modern slavery: classical and Bayesian approaches

Multiple systems estimation is a key approach for quantifying hidden populations such as the number of victims of modern slavery. The UK Government published an estimate of 10,000 to 13,000 victims, constructed by the present author, as part of the strategy leading to the Modern Slavery Act 2015. This estimate was obtained by a stepwise multiple systems method based on six lists. Further investigation shows that a small proportion of the possible models give rather different answers, and that other model fitting approaches may choose one of these. Three data sets collected in the field of modern slavery, together with a data set about the death toll in the Kosovo conflict, are used to investigate the stability and robustness of various multiple systems estimate methods. The crucial aspect is the way that interactions between lists are modelled, because these can substantially affect the results. Model selection and Bayesian approaches are considered in detail, in particular to assess their stability and robustness when applied to real modern slavery data. A new Markov Chain Monte Carlo Bayesian approach is developed; overall, this gives robust and stable results at least for the examples considered. The software and datasets are freely and publicly available to facilitate wider implementation and further research

Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.Comment: 5 pages, 3 Figures, RevTeX4 Introduction expanded, typos correcte

The invertibility of the XOR of rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.

Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on Theoretical Aspects of Rationality and Knowledge (TARK'03

From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.Comment: 22 pages, plain TeX, 9 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages); minor typographical corrections and journal reference adde

Quantum entanglement using trapped atomic spins

We propose an implementation for quantum logic and computing using trapped atomic spins of two different species, interacting via direct magnetic spin-spin interaction. In this scheme, the spins (electronic or nuclear) of distantly spaced trapped neutral atoms serve as the qubit arrays for quantum information processing and storage, and the controlled interaction between two spins, as required for universal quantum computing, is implemented in a three step process that involves state swapping with a movable auxiliary spin.Comment: minor revisions with an updated discussion on adibatic tranportation of trapped qubit, 5 pages, 3 figs, resubmitted to PR

Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results

We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction $\theta$ of a Fisher-von Mises-Langevin distribution on the $p$-dimensional unit hypersphere is equal to a given direction $\theta_0$. After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension $p_n$ goes to infinity at an arbitrary rate with the sample size $n$, and where the concentration $\kappa_n$ behaves in a completely free way with $n$, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of $(\kappa_n)$, that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified $\kappa_n$ and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified $\kappa_n$. To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local asymptotic powers through martingale CLTs in the broader, semiparametric, model of rotationally symmetric distributions. A Monte Carlo study shows that the finite-sample behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure

Security proofs for the MD6 hash function mode of operation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 79-82).In recent years there have been a series of serious and alarming cryptanalytic attacks on several commonly-used hash functions, such as MD4, MD5, SHA-0, and SHA1 [13, 38]. These culminated with the celebrated work of Wang, Yin, and Yu from 2005, which demonstrated relatively efficient methods for finding collisions in the SHA-1 hash function [37]. Although there are several cryptographic hash functions - such as the SHA-2 family [28] - that have not yet succumbed to such attacks, the U.S. National Institute of Standards and Technology (NIST) put out a call in 2007 for candidate proposals for a new cryptographic hash function family, to be dubbed SHA-3 [29]. Hash functions are algorithms for converting an arbitrarily large input into a fixed-length message digest. They are typically composed of a compression function or block cipher that operate on fixed-length pieces of the input and a mode of operation that governs how apply the compression function or block cipher repeatedly on these pieces in order to allow for arbitrary-length inputs. Cryptographic hash functions are furthermore required to have several important and stringent security properties including (but not limited to) first-preimage resistance, second-preimage resistance, collision resistance, and for keyed hash functions, pseudorandomness. This work presents proofs of security for the mode of operation of the MD6 cryptographic hash function [32] - a candidate for the SHA-3 competition - which differs greatly from the modes of operation of many commonly-used hash functions today (MD4, MD5, as well as the SHA family of hash functions.) In particular, we demonstrate provably that the mode of operation used in MD6 preserves some cryptographic properties of the compression function - that is, assuming some ideal conditions about the compression function used, the overall MD6 hash function is secure as well.by Christopher Yale Crutchfield.S.M

Limitations on information-theoretically-secure quantum homomorphic encryption

Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information-theoretically-secure fully homomorphic encryption. Here we show, via an information localization argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required

Quantum homomorphic encryption for circuits of low TT-gate complexity

Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic encryption, which is the encryption of quantum information such that quantum computations can be performed given the ciphertext only. Our schemes allows for arbitrary Clifford group gates, but become inefficient for circuits with large complexity, measured in terms of the non-Clifford portion of the circuit (we use the "$\pi/8$" non-Clifford group gate, which is also known as the $T$-gate). More specifically, two schemes are proposed: the first scheme has a decryption procedure whose complexity scales with the square of the number of $T$-gates (compared with a trivial scheme in which the complexity scales with the total number of gates); the second scheme uses a quantum evaluation key of length given by a polynomial of degree exponential in the circuit's $T$-gate depth, yielding a homomorphic scheme for quantum circuits with constant $T$-depth. Both schemes build on a classical fully homomorphic encryption scheme. A further contribution of ours is to formally define the security of encryption schemes for quantum messages: we define quantum indistinguishability under chosen plaintext attacks in both the public and private-key settings. In this context, we show the equivalence of several definitions. Our schemes are the first of their kind that are secure under modern cryptographic definitions, and can be seen as a quantum analogue of classical results establishing homomorphic encryption for circuits with a limited number of multiplication gates. Historically, such results appeared as precursors to the breakthrough result establishing classical fully homomorphic encryption