Related papers: Pseudorandom unitaries with non-adaptive security
Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm.…
In this paper, we systematically study property testing of unitary operators. We first introduce a distance measure that reflects the average difference between unitary operators. Then we show that, with respect to this distance measure,…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
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 demonstrate quantum algorithms to implement pseudo-random operators that closely reproduce statistical properties of random matrices from the three universal classes: unitary, symmetric, and symplectic. Modified versions of the…
Quantum information processing in the presence of continuous symmetry is of wide importance and exhibits many novel physical and mathematical phenomena. SU(d) is a continuous group of particular interest since it represents a fundamental…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
Introduced in [CG24], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally…
Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary…
We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an $n$-qubit pure state $|\psi\rangle$, we give an efficient algorithm that distinguishes whether…
Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[…
It has been recently proposed that the naive semiclassical prediction of non-unitary black hole evaporation can be understood in the fundamental description of the black hole as a consequence of ignorance of high-complexity information.…
Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…
We show that every correctable subsystem for an arbitrary noise operation can be recovered by a unitary operation, where the notion of recovery is more relaxed than the notion of correction insofar as it does not protect the subsystem from…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal…
Unmanned aerial vehicles (UAVs) are cyber-physical systems whose attack surface spans networked avionics and on-board sensor fusion: a compromised GPS or battery module can mimic a benign mission segment and evade naive anomaly detectors.…
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…