相关论文: Projections of Orbital Measures and Quantum Margin…

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically,…

The goal of this paper is to make a connection between tropical geometry, representations of quantum affine algebras, and scattering amplitudes in physics. The connection allows us to study important and difficult questions in these areas:…

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…

Given a point $A$ in the convex hull of a given adjoint orbit $\mathcal{O}(F)$ of a compact Lie group $G$, we give a polynomial time algorithm to compute the probability density supported on $\mathcal{O}(F)$ whose expectation is $A$ and…

We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…

Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…

We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…

We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…

To some braiding R of Hecke type (a Hecke symmetry) we put into correspondence an associative algebra called the modified Reflection Equation Algebra (mREA). We construct a series of matrices L_(m), m=1,2,... with entries belonging to mREA…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

Quantum resource theories (QRTs) provide a comprehensive and practical framework for the analysis of diverse quantum phenomena. A fundamental task within QRTs is the quantification of resources inherent in a given quantum state. In this…

We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…

Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…

Following our discussion [Physica A, 375 (2007) 123] to associate an analogous probabilistic description with spacetime geometry in the Schwarzschild metric from the macro- to the micro-domain, we argue that there is a possible connection…

This paper investigates the distribution of rational and algebraic points of bounded weighted height in weighted projective spaces over number fields. For a weighted projective space with weights q over a number field k of degree m, we…