Related papers: Quantum limits on post-selected, probabilistic qua…
Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Incompatibility of certain measurements -- impossibility of obtaining deterministic outcomes simultaneously -- is a well known property of quantum mechanics. This feature can be utilized in many contexts, ranging from Bell inequalities to…
We show that postselection offers a nonclassical advantage in metrology. In every parameter-estimation experiment, the final measurement or the postprocessing incurs some cost. Postselection can improve the rate of Fisher information (the…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
Quantum-enhanced metrology surpasses classical metrology by improving estimation precision scaling with a resource $N$ (e.g., particle number or energy) from $1/\sqrt{N}$ to $1/N$. Through the use of nonlinear effects, Roy and…
Quantum metrology aims to enhance measurement precision beyond the classical limit by leveraging quantum resources. Unlike multi-parameter dynamic quantum metrology, many questions regarding multiparameter quantum metrology at thermal…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account,…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error-correction this limitation can be…
Nielsen [quant-ph/0108020] introduced a model of quantum computation by measurement-based simulation of unitary computations. In this model, a consequence of the non-determinism of quantum measurement is the probabilistic termination of…