Quantum process in probability representation of quantum mechanics

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit flipping and amplitude damping processes.

Probability Representation of Quantum States

The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

Properties of Quantizer and Dequantizer Operators for Qudit States and Parametric Down-Conversion

We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are studied in the probability representation of quantum mechanics.

Combining Deep Learning and Survival Analysis for Asset Health Management

We propose a method to integrate feature extraction and prediction as a single optimization task by stacking a three-layer model as a deep learning structure. The first layer of the deep structure is a Long Short Term Memory (LSTM) model which deals with the sequential input data from a group of assets. The output of the LSTM model is followed by meanpooling, and the result is fed to the second layer. The second layer is a neural network layer, which further learns the feature representation. The output of the second layer is connected to a survival model as the third layer for predicting asset health condition. The parameters of the three-layer model are optimized together via stochastic gradient decent. The proposed method was tested on a small dataset collected from a fleet of mining haul trucks. The model resulted in the “individualized” failure probability representation for assessing the health condition of each individual asset, which well separates the in-service and failed trucks. The proposed method was also tested on a large open source hard drive dataset, and it showed promising result.