Related papers: Time Series, Stochastic Processes and Completeness…
We present here a quantum mechanical framework for defining the statistics of measurements of time integrals of A(t), A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed…
We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
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…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
Multi-time quantum processes are endowed with the same richness as multipartite states, including temporal entanglement and exotic causal structures. However, experimentally probing these rich phenomena leans heavily on fast and clean…
It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
Performance of quantum process estimation is naturally limited to fundamental, random, and systematic imperfections in preparations and measurements. These imperfections may lead to considerable errors in the process reconstruction due to…
In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty…
Quantum measurements with feed-forward are crucial components of fault-tolerant quantum computers. We show how the error rate of such a measurement can be directly estimated by fitting the probability that successive randomly compiled…
The development of large-scale platforms for quantum information requires new methods for verification and validation of quantum behavior. Quantum tomography (QT) is the standard tool for diagnosing quantum states, process, and readout…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs' general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must,…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…