Related papers: Pseudorandom Unitaries in the Haar Random Oracle M…
Common random string model is a popular model in classical cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many…
Pseudorandom quantum states (PRS) are efficiently constructible states that are computationally indistinguishable from being Haar-random, and have recently found cryptographic applications. We explore new definitions, new properties and…
We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact…
Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…
We study the (quantum) security of pseudorandom generators (PRGs) constructed from random oracles. We prove a "lifting theorem" showing, roughly, that if such a PRG is unconditionally secure against classical adversaries making polynomially…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
Successive pairs of pseudo-random numbers generated by standard linear congruential transformations display ordered patterns of parallel lines. We study the ``ordered'' and ``chaotic'' distribution of such pairs by solving the eigenvalue…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum…
A recent proposal for a superdeterministic account of quantum mechanics, named Invariant-set theory, appears to bring ideas from several diverse fields like chaos theory, number theory and dynamical systems to quantum foundations. However,…
Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement'', a property exhibited by ensembles of…
We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states.…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…
We show how to construct pseudorandom permutations (PRPs) that remain secure even if the adversary can query the permutation, both in the forward and reverse directions, on a quantum superposition of inputs. Such quantum-secure PRPs have…
In this survey we summarize properties of pseudorandomness and non-randomness of some number-theoretic sequences and present results on their behaviour under the following measures of pseudorandomness: balance, linear complexity,…
Undoing a unitary operation, $i.e$. reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any…
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…