Related papers: Quantum-Proof Extractors: Optimal up to Constant F…
Some, but not all, extractors resist adversaries with limited quantum storage. In this paper we show that Trevisan's extractor has this property, thereby showing an extractor against quantum storage with logarithmic seed length.
We study the problem of extracting randomness from somewhere-random sources, and related combinatorial phenomena: partition analogues of Shearer's lemma on projections. A somewhere-random source is a tuple $(X_1, \ldots, X_t)$ of (possibly…
It is a well-known fact in classical information theory that no deterministic procedure can extract close-to-ideal randomness from an arbitrary entropy source. On the other hand, if additional knowledge about the source is available --…
Standard quantum inference converts quantum data into classical outputs. We study an alternative inference setting in which the desired output is quantum, preserving coherence. Such settings include quantum purity amplification (QPA),…
As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
Self-testing and Semi-Device Independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular for…
Device-independent (DI) quantum cryptography aims at providing secure cryptography with minimal trust in, or characterisation of, the underlying quantum devices. A key step in DI protocols is randomness extraction (or privacy…
We initiate the study of multi-source extractors in the quantum world. In this setting, our goal is to extract random bits from two independent weak random sources, on which two quantum adversaries store a bounded amount of information. Our…
Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers…
For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which…
We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by Kamp, Rao, Vadhan and Zuckerman (STOC'06), and falls into a line of…
We study deterministic extractors for oblivious bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions with small min-entropy: of the function's n input bits, k << n bits are uniformly random and unknown to the…
The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about $1/2$, the other source can have small…
Quantum computing devices can now perform sampling tasks which, according to complexity-theoretic and numerical evidence, are beyond the reach of classical computers. This raises the question of how one can efficiently verify that a quantum…
We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…