Related papers: Hierarchically discriminating Haar-randomness in q…
As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide…
We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed…
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling $t$ copies of a $d$-dimensional quantum state according to the Haar measure on the…
We present a classification algorithm for quantum states, inspired by decision-tree methods. To adapt the decision-tree framework to the probabilistic nature of quantum measurements, we utilize conditional probabilities to compute…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
The emergence of randomness from unitary quantum dynamics is a central problem across diverse disciplines, ranging from the foundations of statistical mechanics to quantum algorithms and quantum computation. Physical systems are invariably…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
We explore the interplay between symmetry and randomness in quantum information. Adopting a geometric approach, we consider states as $H$-equivalent if related by a symmetry transformation characterized by the group $H$. We then introduce…
Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a device-independent scenario using tools of self-testing…
The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates…
Black-box separations are a cornerstone of cryptography, indicating barriers to various goals. A recent line of work has explored black-box separations for quantum cryptographic primitives. Namely, a number of separations are known in the…
Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information…
Producing quantum states at random has become increasingly important in modern quantum science, with applications both theoretical and practical. In particular, ensembles of such randomly-distributed, but pure, quantum states underly our…
Measurements of quantum systems can be used to generate classical data that is truly unpredictable for every observer. However, this true randomness needs to be discriminated from randomness due to ignorance or lack of control of the…
Deep thermalization refers to the emergence of Haar-like randomness from quantum systems upon partial measurements. As a generalization of quantum thermalization, it is often associated with high complexity and entanglement. Here, we…
Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
The emergence of quantum theory at the beginning of 20$-th$ century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a…
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…
In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in…