Related papers: Minimal sufficient statistical experiments on von …
A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al., are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements,…
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space…
Exploiting the tension between the two dynamics of quantum theory (QT) in the Wigner's Friend thought experiment, we point out that the standard QT leads to inconsistency in observed probabilities of measurement outcomes between two…
We introduce the relative Haagerup approximation property for a unital, expected inclusion of arbitrary von Neumann algebras and show that if the smaller algebra is finite then the notion only depends on the inclusion itself, and not on the…
We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
We study existence of minimizers of the least gradient problem \[\inf_{v \in BV_g} \int_{\Omega}\varphi(x, Dv),\] where $BV_g=\{v \in BV(\Omega): \int_{\partial \Omega}gv=1\}$, $\varphi(x,p): \Omega\times \R^n \rightarrow \R$ is a convex,…
We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting…
The present paper is devoted to study of ring isomorphisms of $\ast$-subalgebras of Murray--von Neumann factors. Let $\cM,$ $\cN$ be von Neumann factors of type II$_1,$ and let $S(\cM),$ $S(\cN)$ be the $\ast$-algebras of all measurable…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a much younger subject than phase space formulations of quantum…
Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued…
In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…
We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of minimal sufficient Jordan algebras, which can be seen to…
We propose a physical analogy between finding the solution of an ordinary differential equation (ODE) and a $N$ particle problem in statistical mechanics. It uses the fact that the solution of an ODE is equivalent to obtain the minimum of a…
The discrimination of quantum states is a central problem in quantum information science and technology. Meanwhile, partial post-selection has emerged as a valuable tool for quantum state engineering. In this work, we bring these two areas…
In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a…