相关论文: Voronoi Diagrams for Pure 1-qubit Quantum States

Each platonic solid defines a single-qubit positive operator valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing this kind of measurements and other simple types of…

This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…

We consider the Voronoi diagram of points in the real plane when the distance between two points $a$ and $b$ is given by $L_p(a-b)$ where $L_p((x,y)) = (|x|^p+|y|^p)^{1/p}.$ We prove that the Voronoi diagram has a limit as $p$ converges to…

We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These…

We present a surprisingly simple three-dimensional Bloch sphere representation of a qutrit, i.e., a single three-level quantum system. We start with a symmetric state of a two-qubit system and relate it to the spin-1 representation. Using…

We represent a two-qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the…

There is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are…

The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group;…

We show that for an m-partite quantum system, there is a ball of radius 2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices. This can be used to derive an epsilon below…

Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the…

We study the quantum phase diagrams of Bose-Fermi mixtures of ultracold atoms confined to one dimension in an optical lattice. For systems with incommensurate densities, various quantum phases, e.g. charge/spin density waves, pairing, phase…

We describe a new algorithm for computing the Voronoi diagram of a set of $n$ points in constant-dimensional Euclidean space. The running time of our algorithm is $O(f \log n \log \Delta)$ where $f$ is the output complexity of the Voronoi…

We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a…

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…

Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which…

The circuit model of quantum computation is reformulated as a multilayer network theory [3] called a Quantum Multiverse Network (QuMvN). The QuMvN formulation allows us to interpret the quantum wave function as a combination of ergodic…

The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation…

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…

Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria…

We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform…