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Published work

34 published item(s)

preprint2026arXiv

Evaluating the Utility of Personal Health Records in Personalized Health AI

Patient-managed Personal Health Records (PHRs) promises to empower patients to better understand their health; but information in the record is complex, potentially hindering insights. In this study, we assess the potential of large language models (LLMs, Gemini 3.0 Flash) to provide helpful answers to user health queries, when provided clinical data from PHRs as context. A total of 2,257 user queries were drawn from 3 different distributions to represent patient questions: shorter web search queries, longer questions derived from templates of chatbot conversations, and questions patients asked to their healthcare team (patient calls). Queries were matched with de-identified PHRs (from a pool of 1,945). Gemini responses were generated (1) without PHR context; (2) with a basic summary of demographics, conditions, and medications; (3) with full, extensive clinical notes. For evaluation, we leveraged an existing rating framework (SHARP), and developed a new framework for specific error modes when interpreting PHRs. Evaluation was performed using autoraters for the full set, and with clinician ratings for a subset (n=95), with both sets of raters knowing the full PHR context. We see significant improvements in the helpfulness of answers to all question types with PHR data (p < 0.001, paired t-test). We also observe potential gains in safety, accuracy, relevance and personalization of answers. Our PHR evaluation framework further identifies gaps in LLM understanding of particular aspects of complex PHRs, such as temporal disorientation, and rare but meaningful confabulations. These results suggest potential for PHR data to help people with a wide range of user needs; and provide a framework for monitoring for gaps in LLM answers based on PHR context. This study motivates further work to assess and realize potential benefits to users from understanding their health records.

preprint2022arXiv

Dynamic Planning in Open-Ended Dialogue using Reinforcement Learning

Despite recent advances in natural language understanding and generation, and decades of research on the development of conversational bots, building automated agents that can carry on rich open-ended conversations with humans "in the wild" remains a formidable challenge. In this work we develop a real-time, open-ended dialogue system that uses reinforcement learning (RL) to power a bot's conversational skill at scale. Our work pairs the succinct embedding of the conversation state generated using SOTA (supervised) language models with RL techniques that are particularly suited to a dynamic action space that changes as the conversation progresses. Trained using crowd-sourced data, our novel system is able to substantially exceeds the (strong) baseline supervised model with respect to several metrics of interest in a live experiment with real users of the Google Assistant.

preprint2022arXiv

The Large Core of College Admission Markets: Theory and Evidence

We study stable allocations in college admissions markets where students can attend the same college under different financial terms. The deferred acceptance algorithm identifies a stable allocation where funding is allocated based on merit. While merit-based stable allocations assign the same students to college, non-merit-based stable allocations may differ in the number of students assigned to college. In large markets, this possibility requires heterogeneity in applicants' sensitivity to financial terms. In Hungary, where such heterogeneity is present, a non-merit-based stable allocation would increase the number of assigned applicants by 1.9%, and affect 8.3% of the applicants relative to any merit-based stable allocation. These findings contrast sharply with findings from the matching (without contracts) literature.

preprint2022arXiv

TRUE: Re-evaluating Factual Consistency Evaluation

Grounded text generation systems often generate text that contains factual inconsistencies, hindering their real-world applicability. Automatic factual consistency evaluation may help alleviate this limitation by accelerating evaluation cycles, filtering inconsistent outputs and augmenting training data. While attracting increasing attention, such evaluation metrics are usually developed and evaluated in silo for a single task or dataset, slowing their adoption. Moreover, previous meta-evaluation protocols focused on system-level correlations with human annotations, which leave the example-level accuracy of such metrics unclear. In this work, we introduce TRUE: a comprehensive survey and assessment of factual consistency metrics on a standardized collection of existing texts from diverse tasks, manually annotated for factual consistency. Our standardization enables an example-level meta-evaluation protocol that is more actionable and interpretable than previously reported correlations, yielding clearer quality measures. Across diverse state-of-the-art metrics and 11 datasets we find that large-scale NLI and question generation-and-answering-based approaches achieve strong and complementary results. We recommend those methods as a starting point for model and metric developers, and hope TRUE will foster progress towards even better evaluation methods.

preprint2021arXiv

Planning and Learning with Stochastic Action Sets

In many practical uses of reinforcement learning (RL) the set of actions available at a given state is a random variable, with realizations governed by an exogenous stochastic process. Somewhat surprisingly, the foundations for such sequential decision processes have been unaddressed. In this work, we formalize and investigate MDPs with stochastic action sets (SAS-MDPs) to provide these foundations. We show that optimal policies and value functions in this model have a structure that admits a compact representation. From an RL perspective, we show that Q-learning with sampled action sets is sound. In model-based settings, we consider two important special cases: when individual actions are available with independent probabilities; and a sampling-based model for unknown distributions. We develop poly-time value and policy iteration methods for both cases; and in the first, we offer a poly-time linear programming solution.

preprint2020arXiv

Adversarially Robust Streaming Algorithms via Differential Privacy

A streaming algorithm is said to be adversarially robust if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an adaptive adversary. We establish a connection between adversarial robustness of streaming algorithms and the notion of differential privacy. This connection allows us to design new adversarially robust streaming algorithms that outperform the current state-of-the-art constructions for many interesting regimes of parameters.

preprint2020arXiv

An Optimal Elimination Algorithm for Learning a Best Arm

We consider the classic problem of $(ε,δ)$-PAC learning a best arm where the goal is to identify with confidence $1-δ$ an arm whose mean is an $ε$-approximation to that of the highest mean arm in a multi-armed bandit setting. This problem is one of the most fundamental problems in statistics and learning theory, yet somewhat surprisingly its worst-case sample complexity is not well understood. In this paper, we propose a new approach for $(ε,δ)$-PAC learning a best arm. This approach leads to an algorithm whose sample complexity converges to \emph{exactly} the optimal sample complexity of $(ε,δ)$-learning the mean of $n$ arms separately and we complement this result with a conditional matching lower bound. More specifically:

preprint2016arXiv

Concentration Inequalities for Random Sets

In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population is defined as the difference between the number of reds in it and p times its size. This paper presents high-probability upper bounds (tail-bounds) on this imbalance. To present the upper bounds we define the *UI dimension* --- a new measure for the richness of a set-family. We present three simple rules for upper-bounding the UI dimension of a set-family. Our upper bounds on the imbalance in a sub-population depend only on the size of the sub-population and on the UI dimension of its support. We relate our results to known concepts from machine learning, particularly the VC dimension and Rademacher complexity.

preprint2016arXiv

Demand-Flow of Agents with Gross-Substitute Valuations

We consider the class of valuations on indivisible items called gross-substitute (GS). This class was introduced by Kelso and Crawford (1982) and is widely used in studies of markets with indivisibilities. GS is a condition on the demand-flow in a specific scenario: some items become more expensive while other items retain their price. We prove that GS implies a much stronger condition, describing the demand-flow in the general scenario in which all prices may change. We prove that the demand of GS agents always flows (weakly) downwards, i.e, from items with higher price-increase to items with lower price-increase. We show that this property is equivalent to GS and is not true when there are complementarities.

preprint2016arXiv

SBBA: a Strongly-Budget-Balanced Double-Auction Mechanism

In a seminal paper, McAfee (1992) presented the first dominant strategy truthful mechanism for double auction. His mechanism attains nearly optimal gain-from-trade when the market is sufficiently large. However, his mechanism may leave money on the table, since the price paid by the buyers may be higher than the price paid to the sellers. This money is included in the gain-from-trade and in some cases it accounts for almost all the gain-from-trade, leaving almost no gain-from-trade to the traders. We present SBBA: a variant of McAfee's mechanism which is strongly budget-balanced. There is a single price, all money is exchanged between buyers and sellers and no money is left on the table. This means that all gain-from-trade is enjoyed by the traders. We generalize this variant to spatially-distributed markets with transit costs.

preprint2016arXiv

Submodular Optimization under Noise

We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable approximation guarantees. In many applications, however, we do not have access to the submodular function we aim to optimize, but rather to some erroneous or noisy version of it. This raises the question of whether provable guarantees are obtainable in presence of error and noise. We provide initial answers, by focusing on the question of maximizing a monotone submodular function under a cardinality constraint when given access to a noisy oracle of the function. We show that: - For a cardinality constraint $k \geq 2$, there is an approximation algorithm whose approximation ratio is arbitrarily close to $1-1/e$; - For $k=1$ there is an algorithm whose approximation ratio is arbitrarily close to $1/2$. No randomized algorithm can obtain an approximation ratio better than $1/2+o(1)$; -If the noise is adversarial, no non-trivial approximation guarantee can be obtained.

preprint2015arXiv

Optimistic-Conservative Bidding in Sequential Auctions

In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both linear and unit demand valuations, the only pure subgame perfect equilibrium where buyers are bidding in an optimistic conservative manner is the minimal Walrasian equilibrium. In addition, we show examples where without the requirement of conservative bidding, subgame perfect equilibria can admit a variety of unlikely predictions, including high price of anarchy and low revenue in markets composed of additive bidders, equilibria which elicit all the surplus as revenue, and more. We also show that the order in which the items are sold can influence the outcome.

preprint2015arXiv

Sorting and Selection with Imprecise Comparisons

We consider a simple model of imprecise comparisons: there exists some $δ>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $δ$, then the comparison will be made correctly; when the two elements have values that are within $δ$, the outcome of the comparison is unpredictable. This model is inspired by both imprecision in human judgment of values and also by bounded but potentially adversarial errors in the outcomes of sporting tournaments. Our model is closely related to a number of models commonly considered in the psychophysics literature where $δ$ corresponds to the {\em just noticeable difference unit (JND)} or {\em difference threshold}. In experimental psychology, the method of paired comparisons was proposed as a means for ranking preferences amongst $n$ elements of a human subject. The method requires performing all $\binom{n}{2}$ comparisons, then sorting elements according to the number of wins. The large number of comparisons is performed to counter the potentially faulty decision-making of the human subject, who acts as an imprecise comparator. We show that in our model the method of paired comparisons has optimal accuracy, minimizing the errors introduced by the imprecise comparisons. However, it is also wasteful, as it requires all $\binom{n}{2}$. We show that the same optimal guarantees can be achieved using $4 n^{3/2}$ comparisons, and we prove the optimality of our method. We then explore the general tradeoff between the guarantees on the error that can be made and number of comparisons for the problems of sorting, max-finding, and selection. Our results provide strong lower bounds and close-to-optimal solutions for each of these problems.

preprint2014arXiv

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion.

preprint2014arXiv

Local computation mechanism design

We introduce the notion of Local Computation Mechanism Design - designing game theoretic mechanisms which run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. In addition, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanisms need to maintain incentive compatibility with respect to the allocation and payments. We present local computation mechanisms for a variety of classical game-theoretical problems: 1. stable matching, 2. job scheduling, 3. combinatorial auctions for unit-demand and k-minded bidders, and 4. the housing allocation problem. For stable matching, some of our techniques may have general implications. Specifically, we show that when the men's preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

preprint2014arXiv

Probe Scheduling for Efficient Detection of Silent Failures

Most discovery systems for silent failures work in two phases: a continuous monitoring phase that detects presence of failures through probe packets and a localization phase that pinpoints the faulty element(s). This separation is important because localization requires significantly more resources than detection and should be initiated only when a fault is present. We focus on improving the efficiency of the detection phase, where the goal is to balance the overhead with the cost associated with longer failure detection times. We formulate a general model which unifies the treatment of probe scheduling mechanisms, stochastic or deterministic, and different cost objectives - minimizing average detection time (SUM) or worst-case detection time (MAX). We then focus on two classes of schedules. {\em Memoryless schedules} -- a subclass of stochastic schedules which is simple and suitable for distributed deployment. We show that the optimal memorlyess schedulers can be efficiently computed by convex programs (for SUM objectives) or linear programs (for MAX objectives), and surprisingly perhaps, are guaranteed to have expected detection times that are not too far off the (NP hard) stochastic optima. {\em Deterministic schedules} allow us to bound the maximum (rather than expected) cost of undetected faults, but like stochastic schedules, are NP hard to optimize. We develop novel efficient deterministic schedulers with provable approximation ratios. An extensive simulation study on real networks, demonstrates significant performance gains of our memoryless and deterministic schedulers over previous approaches. Our unified treatment also facilitates a clear comparison between different objectives and scheduling mechanisms.

preprint2013arXiv

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time $\tilde{O}(2^k \poly(k) M n^ω) = O^*(2^k M)$. If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of $\tilde{O}(2^k \poly(k) n^ω(\log\log M + 1/\varepsilon))$. For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time $\tilde{O}(2^k \poly(k) M n^3) $ and a $(1+\varepsilon)$-approximate solution of running time $\tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon))$. All of the above algorithms are randomized with a polynomially-small error probability.

preprint2013arXiv

Quantum Refrigerator

We consider fault-tolerant quantum computation in the context where there are no fresh ancilla qubits available during the computation, and where the noise is due to a general quantum channel. We show that there are three classes of noisy channels: In the first, typified by the depolarizing channel, computation is only possible for a logarithmic time. In the second class, of which the dephasing channel is an example, computation is possible for polynomial time. The amplitude damping channel is an example of the third class, and for this class of channels, it is possible to compute for an exponential time in the number of qubits available.

preprint2012arXiv

Computing Socially-Efficient Cake Divisions

We consider a setting in which a single divisible good ("cake") needs to be divided between n players, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions that maximize the social welfare, focusing on divisions where each player needs to get one contiguous piece of the cake. We show that for both the utilitarian and the egalitarian social welfare functions it is NP-hard to find the optimal division. For the utilitarian welfare, we provide a constant factor approximation algorithm, and prove that no FPTAS is possible unless P=NP. For egalitarian welfare, we prove that it is NP-hard to approximate the optimum to any factor smaller than 2. For the case where the number of players is small, we provide an FPT (fixed parameter tractable) FPTAS for both the utilitarian and the egalitarian welfare objectives.

preprint2012arXiv

Joint Cache Partition and Job Assignment on Multi-Core Processors

Multicore shared cache processors pose a challenge for designers of embedded systems who try to achieve minimal and predictable execution time of workloads consisting of several jobs. To address this challenge the cache is statically partitioned among the cores and the jobs are assigned to the cores so as to minimize the makespan. Several heuristic algorithms have been proposed that jointly decide how to partition the cache among the cores and assign the jobs. We initiate a theoretical study of this problem which we call the joint cache partition and job assignment problem. By a careful analysis of the possible cache partitions we obtain a constant approximation algorithm for this problem. For some practical special cases we obtain a 2-approximation algorithm, and show how to improve the approximation factor even further by allowing the algorithm to use additional cache. We also study possible improvements that can be obtained by allowing dynamic cache partitions and dynamic job assignments. We define a natural special case of the well known scheduling problem on unrelated machines in which machines are ordered by "strength". Our joint cache partition and job assignment problem generalizes this scheduling problem which we think is of independent interest. We give a polynomial time algorithm for this scheduling problem for instances obtained by fixing the cache partition in a practical case of the joint cache partition and job assignment problem where job loads are step functions.

preprint2012arXiv

Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure

We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using $O(n^{2+\logω})$ queries, where $ω$ is independent of $n$ and depends only on the type of subformulas within the tree. We also prove a classical lower bound of $n^{Ω(\log\log n)}$ queries, thus showing a (small) super-polynomial speed-up.

preprint2012arXiv

Topology Discovery of Sparse Random Graphs With Few Participants

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.

preprint2011arXiv

An Efficient Partitioning Oracle for Bounded-Treewidth Graphs

Partitioning oracles were introduced by Hassidim et al. (FOCS 2009) as a generic tool for constant-time algorithms. For any epsilon > 0, a partitioning oracle provides query access to a fixed partition of the input bounded-degree minor-free graph, in which every component has size poly(1/epsilon), and the number of edges removed is at most epsilon*n, where n is the number of vertices in the graph. However, the oracle of Hassidimet al. makes an exponential number of queries to the input graph to answer every query about the partition. In this paper, we construct an efficient partitioning oracle for graphs with constant treewidth. The oracle makes only O(poly(1/epsilon)) queries to the input graph to answer each query about the partition. Examples of bounded-treewidth graph classes include k-outerplanar graphs for fixed k, series-parallel graphs, cactus graphs, and pseudoforests. Our oracle yields poly(1/epsilon)-time property testing algorithms for membership in these classes of graphs. Another application of the oracle is a poly(1/epsilon)-time algorithm that approximates the maximum matching size, the minimum vertex cover size, and the minimum dominating set size up to an additive epsilon*n in graphs with bounded treewidth. Finally, the oracle can be used to test in poly(1/epsilon) time whether the input bounded-treewidth graph is k-colorable or perfect.

preprint2011arXiv

Non-Price Equilibria in Markets of Discrete Goods

We study markets of indivisible items in which price-based (Walrasian) equilibria often do not exist due to the discrete non-convex setting. Instead we consider Nash equilibria of the market viewed as a game, where players bid for items, and where the highest bidder on an item wins it and pays his bid. We first observe that pure Nash-equilibria of this game excatly correspond to price-based equilibiria (and thus need not exist), but that mixed-Nash equilibria always do exist, and we analyze their structure in several simple cases where no price-based equilibrium exists. We also undertake an analysis of the welfare properties of these equilibria showing that while pure equilibria are always perfectly efficient ("first welfare theorem"), mixed equilibria need not be, and we provide upper and lower bounds on their amount of inefficiency.

preprint2011arXiv

Quantum state restoration and single-copy tomography

Given a single copy of an n qubit quantum state |psi>, the no-cloning theorem greatly limits the amount of information which can be extracted from it. Moreover, given only a procedure which verifies the state, for example a procedure which measures the operator |psi><psi|, we cannot prepare |psi> in time polynomial in n . In this paper, we consider the scenario in which we are given both a single copy of |psi> and the ability to verify it. We show that in this setting, we can do several novel things efficiently. We present a new algorithm that we call quantum state restoration which allows us to extend a large subsystem of |psi> to the full state, and in turn this allows us to copy small subsystems of |psi>. In addition, we present algorithms that can perform tomography on small subsystems of |psi>, and we show how to use these algorithms to estimate the statistics of any efficiently implementable POVM acting on |psi> in time polynomial in the number of outcomes of the POVM.

preprint2010arXiv

Matching with Couples Revisited

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.

preprint2010arXiv

Quantum money from knots

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.

preprint2009arXiv

Adaptive versus non-adaptive strategies for quantum channel discrimination

We provide a simple example that illustrates the advantage of adaptive over non-adaptive strategies for quantum channel discrimination. In particular, we give a pair of entanglement-breaking channels that can be perfectly discriminated by means of an adaptive strategy that requires just two channel evaluations, but for which no non-adaptive strategy can give a perfect discrimination using any finite number of channel evaluations.

preprint2009arXiv

Breaking and making quantum money: toward a new quantum cryptographic protocol

Public-key quantum money is a cryptographic protocol in which a bank can create quantum states which anyone can verify but no one except possibly the bank can clone or forge. There are no secure public-key quantum money schemes in the literature; as we show in this paper, the only previously published scheme [1] is insecure. We introduce a category of quantum money protocols which we call collision-free. For these protocols, even the bank cannot prepare multiple identical-looking pieces of quantum money. We present a blueprint for how such a protocol might work as well as a concrete example which we believe may be insecure.

preprint2009arXiv

Global Alignment of Molecular Sequences via Ancestral State Reconstruction

Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on substitution-only models of sequence evolution. In practice these methods are extended beyond this simplified setting with the use of heuristics that produce global alignments of the input sequences--an important problem which has no rigorous model-based solution. In this paper we consider a new version of the multiple sequence alignment in the context of stochastic indel models. More precisely, we introduce the following {\em trace reconstruction problem on a tree} (TRPT): a binary sequence is broadcast through a tree channel where we allow substitutions, deletions, and insertions; we seek to reconstruct the original sequence from the sequences received at the leaves of the tree. We give a recursive procedure for this problem with strong reconstruction guarantees at low mutation rates, providing also an alignment of the sequences at the leaves of the tree. The TRPT problem without indels has been studied in previous work (Mossel 2004, Daskalakis et al. 2006) as a bootstrapping step towards obtaining optimal phylogenetic reconstruction methods. The present work sets up a framework for extending these works to evolutionary models with indels.

preprint2009arXiv

Quantum algorithms for testing properties of distributions

Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the L_1-norm ? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the L_1-distance between P and Q can be estimated with a constant precision using approximately N^{1/2} queries in the quantum settings, whereas classical computers need Ω(N) queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity O(N^{1/3}). The classical query complexity of these problems is known to be Ω(N^{1/2}).

preprint2008arXiv

Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority

Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the sole assumption that some number of them will follow the protocol honestly. This paper investigates how much trust is necessary -- that is, how many players must remain honest -- in order for distributed quantum computations to be possible. We present a verifiable quantum secret sharing (VQSS) protocol, and a general secure multiparty quantum computation (MPQC) protocol, which can tolerate any (n-1)/2 (rounded down) cheaters among n players. Previous protocols for these tasks tolerated (n-1)/4 (rounded down) and (n-1)/6 (rounded down) cheaters, respectively. The threshold we achieve is tight - even in the classical case, ``fair'' multiparty computation is not possible if any set of n/2 players can cheat. Our protocols rely on approximate quantum error-correcting codes, which can tolerate a larger fraction of errors than traditional, exact codes. We introduce new families of authentication schemes and approximate codes tailored to the needs of our protocols, as well as new state purification techniques along the lines of those used in fault-tolerant quantum circuits.

preprint2007arXiv

Quantum Search in an Ordered List via Adaptive Learning

We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a noisy answer is returned We present a (classic) algorithm which optimally solves both variants together, up to an additive term of O(\log \log(n)), and prove matching information theoretic lower bounds. We use the algorithm to improve the results of Farhi et al \cite{FGGS99} presenting a quantum (error free) search algorithm in an ordered list of expected complexity less than (\log_2n) / 3.