Related papers: Hierarchically discriminating Haar-randomness in q…

Due to the superiority of quantum computing, traditional cryptography is facing severe threat. This makes the security evaluation of cryptographic systems in quantum attack models significant and urgent. For symmetric ciphers, the security…

Benchmarking quantum devices is a foundational task for the sustained development of quantum technologies. However, accurate in situ characterization of large-scale quantum devices remains a formidable challenge: such systems experience…

Random unitary circuits have become a model system to investigate information scrambling in quantum systems. In the literature, mostly random circuits with Haar-distributed gate operations have been considered. In this work, we investigate…

Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…

We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a…

The need of discriminating between different quantum states is a fundamental issue in Quantum Information and Communication. The actual realization of generally optimal strategies in this task is often limited by the need of supplemental…

Any set of pure states living in an given Hilbert space possesses a natural and unique metric --the Haar measure-- on the group $U(N)$ of unitary matrices. However, there is no specific measure induced on the set of eigenvalues $\Delta$ of…

The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography,…

We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar…

In higher-order quantum computing (HOQC), one typically considers the universal transformation of unknown quantum operations, treated as blackboxes. It is also implicitly assumed that the resulting operation must act on arbitrary, and thus…

There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…

The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In…

The discrimination of quantum operations has long been an intriguing challenge, with theoretical research significantly advancing our understanding of the quantum features in discriminating quantum objects. This challenge is closely related…

Quantum theory allows for randomness generation in a device-independent setting, where no detailed description of the experimental device is required. Here we derive a general upper bound on the amount of randomness that can be generated in…

We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…

A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…

Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize…

In this article we extend results from our previous work [Bendersky, de la Torre, Senno, Figueira and Ac\'in, Phys. Rev. Lett. 116, 230406 (2016)] by providing a protocol to distinguish in finite time and with arbitrarily high success…

Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly…