相关论文: Asymptotic Spectral Measures: Between Quantum Theo…
The incompatibility of quantum measurements is a fundamental feature of quantum mechanics with profound implications for uncertainty relations and quantum information processing. In this paper, we extend the notion of {\em $s$-order…
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their $d^2$-outcomes are enough to reconstruct any $d$-dimensional quantum state.…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The aim of this paper is to show a connection between an extended theory of statistical experiments on the one hand and the foundation of quantum theory on the other hand. The main aspects of this extension are: One assumes a hyperparameter…
Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored.…
This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and…
A theorem of Davies states that for symmetric quantum states there exists a symmetric POVM maximizing the mutual information. To apply this theorem the representation of the symmetry group has to be irreducible. We obtain a similar yet…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
We suggest several mathematical counterparts to the idea of "effective degrees of freedom" and formulate specific questions, much of which are inspired by Larry Guth's results and ideas on the Hermann Weyl kind of asymptotics of the Morse…
The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
We propose a new structure of ensembles in quantum theory, based on the recently introduced intrinsic properties of electrons and photons. On this statistical basis the spreading of a wave-packet, collapse of the wave function, the quantum…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
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…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with…
Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs $(X_t,X_{t-k})$ in a…
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…