Related papers: Quantum Mechanical View of Mathematical Statistics
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an $n$-qubit state $\psi$ consists of its inner products with $O(\sqrt{2^n})$ stabilizer…
In this contribution, we aim to illustrate how quantum work statistics can be used as a tool in order to gain insight on the universal features of non-equilibrium many-body systems. Focusing on the two point measurement approach to work, we…
The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement,…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Given a density operator $\hat \rho$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat \rho}(X,\phi),\ \phi \in [0,2\pi),$ on the real line allowing to reconstruct $\hat \rho $. We introduce a dual…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
In a newly introduced time scale $\tau$, much smaller than the usual $t$, any object is assumed to be a point-like particle, having a definite position. It fluctuates without dynamics and the wave function $\Psi$ is defined by averaging the…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
The quantum measurement problem, understanding why a unique outcome is obtained in each individual experiment, is tackled by solving models. After an introduction we review the many dynamical models proposed over the years. A flexible and…
Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e.,…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
A theory of quantum measurement was introduced some time ago that was based on the notion of the so-called separation status. This separation status had a spatial, local character, so that the theory worked only in special cases.…
We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
A generic unital positive operator-valued measure (POVM), which transforms a given stationary pure state to an arbitrary statistical state with perfect decoherence, is presented. This allows one to operationally realize thermalization as a…