Related papers: Generalized geometric speed limits for quantum obs…
Recently, variational quantum metrology was proposed for Hamiltonians with multiplicative parameters, wherein the estimation precision can be optimized via variational circuits. However, systems with generic Hamiltonians still lack these…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly…
Continuous quantum metrology holds promise for realizing high-precision sensing by harnessing information progressively carried away by the radiation quanta emitted into the environment. Despite recent progress, a comprehensive…
Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution. Most known quantum speed limits, including the celebrated Mandelstam-Tamm and…
Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
Quantum speed limit (QSL) is a fundamental concept in quantum mechanics and provides a lower bound on the evolution time. The attainability of QSL, greatly depending on the understanding of QSL, is a long-standing open problem especially…
Dynamical measurement schemes are an important tool for the investigation of quantum many-body systems, especially in the age of quantum simulation. Here, we address the question whether generic measurements can be implemented efficiently…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…