相关论文: Martingale Models for Quantum State Reduction
We consider the energy-driven stochastic state vector reduction equation for the density matrix, which for pure state density matrices can be written in two equivalent forms. We use these forms to discuss the decoupling of the noise terms…
Stochastic unraveling schemes are powerful computational tools for simulating Lindblad equations, offering significant reductions in memory requirements. However, this advantage is accompanied by increased stochastic uncertainty, and the…
A theory of quantum state reduction is advanced. It is based on two principles: (1) Gauge decomposition; (2) Maximum entropy. To wit: (1) The reduction decomposition of a state vector is the Schmidt decomposition with respect to the states…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…
As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
Enhancing precision sensors for stochastic signals using quantum techniques is a promising emerging field of physics. Estimating a weak stochastic waveform is the core task of many fundamental physics experiments including searches for…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Smoothing is a technique that estimates the state of a system using measurement information both prior and posterior to the estimation time. Two notable examples of this technique are the Rauch-Tung-Striebel and Mayne-Fraser-Potter…
We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the…
This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation, which captures both unitary evolution and environmental dissipation. We develop an energy minimization framework…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…