Related papers: Measurement partitioning and observational equival…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
To effectively utilize quantum incompatibility as a resource in quantum information processing, it is crucial to evaluate how incompatible a set of devices is. In this study, we propose an ordering to compare incompatibility and reveal its…
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible…
This work applies a quantitative metric well-known to the data assimilation community to a new context in order to capture the relative representativeness of non-simultaneous or non-co-located observations and quantify how these…
Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review…
Measure and integral are two closely related, but distinct objects of study. Nonetheless, they are both real-valued lattice valuations: order preserving real-valued functions $\phi$ on a lattice $L$ which are modular, i.e.,…
Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…
State and parameter estimation is essential for process monitoring and control. Observability plays an important role in both state and parameter estimation. In simultaneous state and parameter estimation, the parameters are often augmented…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, properties that make such an interpretation possible rely on the assumption of ideal projective measurements. We show…
In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only…
The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or…
We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of…
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems…
Analysing Quantum Measurement requires analysing the physics of amplification since amplification of phenomena from one scale to another scale is essential to measurement. There still remains the task of working this into an axiomatic…