A tomographic setting for quasi-distribution functions

超导体-半导体 transmons 量子比特中相互作用的马约拉纳态与安德烈夫态的层析特征

Tomographic Signatures of Interacting Majorana and Andreev States in Superconductor-Semiconductor Transmon Qubits

本文研究超导体-半导体 transmons 量子比特中基态结库珀对电荷分布的层析重建，提出通过电荷态概率分布特征识别相互作用态与拓扑态，并利用信息论指标分类结中激发类型差异。

Tomography in Loop Quantum Cosmology

We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schrödinger cat states, and then, by applying a Radon integral transform for those Wigner functions, we are able to obtain the symplectic tomograms which define measurable probability distributions that fully characterize the quantum model of our interest. By appropriately introducing the quantum dispersion for a rotated and squeezed quadrature operator in terms of the position a…

Wigner function and the probability representation of quantum states

The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner--Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of…

Universal ultrabright source of entangled photon states: generation and tomographic analysis of Werner states and of Maximally Entangled Mixed States

A novel ultrabright parametric source of polarization entangled photon pairs with striking spatial characteristics is reported. The distribution of the output electromagnetic k-modes excited by Spontaneous Parametris Down Conversion and coupled to the output detectors can be very broad. It could coincide with the full set of phase-matched excited modes, at least in principle. In this case a relevant conditional quasi-pure output state should be realized. By these (approximate) states realized over a full Entanglement-Ring output distribution, the non local properties of the generated entanglem…

Generic pure quantum states as steady states of quasi-local dissipative dynamics

We investigate whether a generic multipartite pure state can be the unique asymptotic steady state of locality-constrained purely dissipative Markovian dynamics. In the simplest tripartite setting, we show that the problem is equivalent to characterizing the solution space of a set of linear equations and establish that the set of pure states obeying the above property has either measure zero or measure one, solely depending on the subsystems' dimension. A complete analytical characterization is given when the central subsystem is a qubit. In the N-partite case, we provide conditions on the su…

量子光的经典模型中的Wigner函数负值

Wigner function negativity in a classical model of quantum light

本文提出一个经典模型，通过后选择检测事件再现单光子加 coherent 状态的非经典行为，并展示Wigner函数的负值特征。

Superposition rule and entanglement in diagonal and probability representations of density states

The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the probability representation of quantum mechanics is reviewed. The connection of the diagonal and probability representations is discussed. The superposition rule is considered in terms of the density-operator symbols. The separability and entanglement properties of multipartite quantum systems are formulated as the properties of the density-operator symbols of the sys…

准经典设定下的Alicki-Fannes-Winter技术：高级版本及其应用

The Alicki-Fannes-Winter technique in the quasi-classical settings: advanced version and its applications

本文提出了一种高级版本的AFW技术，用于获得量子系统和离散随机变量特征的下半连续性界、连续性界和局部下界，并展示了其在von Neumann熵等量子系统基本特征上的应用。

连续变量的协变算符基

Covariant operator bases for continuous variables

针对连续变量系统，提出一种在辛变换下表现良好的协变算符基，其展开系数以简洁协变形式描述量子态，并用于评估量子性、高斯性及连接层析测量与准概率分布重构。

Probability representation of quantum mechanics and star product quantization

The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in Hilbert space onto these functions is presented. Examples of the Wigner-Weyl symbols (like Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified with the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators which are needed to construct the bij…

From f-divergence to quantum quasi-entropies and their use

Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum generalization is called quasi-entropy which is related to some other important concepts as covariance, quadratic costs, Fisher information, Cramer-Rao inequality and uncertainty relation. A conjecture about the scalar curvature of a Fisher information geometry is explained. The described subjects are overviewed in details in the matrix setting, but at the very end the …