相关论文: A Topos Perspective on the Kochen-Specker Theorem:…
When it isn't possible to tell two distinct experimental procedures apart purely from their input/output statistics, then it seems a plausible hypothesis that the two procedures must be physically identical. We call such a hypothesis…
We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct…
Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…
In recent years, modeling and analysis of interval-valued time series have garnered increasing attention in econometrics, finance, and statistics. However, these studies have predominantly focused on statistical inference in the forecasting…
I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued…
In studies of quantum squeezing, the emphasis is typically placed more on specific squeezed states and their evolution rather than on the dynamical operations that could simultaneously squeeze a broader range of quantum states, regardless…
We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine, under a mild assumption on the distribution, the…
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, when understood as a resource for quantum…
We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with…
Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis,…
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with quantum channels. The result is a convex,…
In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani, and topos quantum theory, as developed by Isham, Butterfield and Doring, amongst others. Towards this end, we…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
For a set $M$ of $m$ elements, we define a decreasing chain of classes of normalized monotone-increasing valuation functions from $2^M$ to $\mathbb{R}_{\geq 0}$, parameterized by an integer $q \in [2,m]$. For a given $q$, we refer to the…