相关论文: Quantum filtering: a reference probability approac…
This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
We extend the optimal filtering equation known from the Stratonovich filtering theory on the quantum process case. The used observation model is based on an indirect measurement method, where the measurement is performed on an ancilla…
A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of…
A *-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an infinitely dimensional nuclear…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
Quantum state filtering is a variant of the unambiguous state discrimination problem: the states are grouped in sets and we want to determine to which particular set a given input state belongs.The simplest case, when the N given states are…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
This paper is concerned with a filtering problem for a class of nonlinear quantum stochastic systems with multichannel nondemolition measurements. The system-observation dynamics are governed by a Markovian Hudson-Parthasarathy quantum…
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden…
Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan $P$ function, also denoted as nonclassicality quasiprobability.…
We analyze time-of-arrival probability distributions for relativistic particles in the context of quantum field theory (QFT). We show that QFT leads to a unique prediction, modulo post-selection that incorporates properties of the apparatus…
In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In…
The quantum theories of boson and fermion fields with quadratic nonstationary Hamiltoanians are rigorously constructed. The representation of the algebra of observables is given by the Hamiltonian diagonalization procedure. The sufficient…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter…