Related papers: Quantum Lifting for Invertible Permutations and Id…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
Security for machine learning has begun to become a serious issue for present day applications. An important question remaining is whether emerging quantum technologies will help or hinder the security of machine learning. Here we discuss a…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
Tamper-resilient cryptography studies how to protect data against adversaries who can physically manipulate codewords before they are decoded. The notion of tamper detection codes formalizes this goal, requiring that any unauthorized…
We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first…
Most currently used cryptographic tools for protecting data are based on certain computational assumptions, which makes them vulnerable with respect to technological and algorithmic developments, such as quantum computing. One existing…
The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…
Quantum key distribution is the most well-known application of quantum cryptography. Previous proposed proofs of security of quantum key distribution contain various technical subtleties. Here, a conceptually simpler proof of security of…
Lifting theorems are theorems that relate the query complexity of a function $f:\{0,1\}^{n}\to\{0,1\}$ to the communication complexity of the composed function $f \circ g^{n}$, for some "gadget" $g:\{0,1\}^{b}\times\{0,1\}^{b}\to\{0,1\}$.…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even…
In symmetric cryptanalysis, the model of superposition queries has led to surprising results, with many constructions being broken in polynomial time thanks to Simon's period-finding algorithm. But the practical implications of these…
Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
We show that the Mayers-Shor-Preskill approach and Renner's approach to proving the security of quantum key distribution (QKD) are essentially the same. We begin our analysis by considering a special case of QKD called privacy amplification…