Related papers: Non-representable quantum measures
Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpanding. Mardare, Panangaden and Plotkin introduced 1-basic varieties as categories of quantitative algebras presented by quantitative equations.…
Generalized quantum measurements are an important extension of projective or von Neumann measurements, in that they can be used to describe any measurement that can be implemented on a quantum system. We describe how to realize two…
Let $\Lambda$ be the set of partitions of length $\geq 0$. We introduce an $\mathbb{N}$-graded algebra $\mathbb{A}_q^d(\Lambda)$ associated to $\Lambda$, which can be viewed as a quantization of the algebra of partitions defined by Reineke.…
Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure on this space defined on the $\sigma$-algebra generated by open subsets of $\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of $\mathcal{X}$.…
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…
We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be…
It is well known that every bivariate copula induces a positive measure on the Borel $\sigma$-algebra on $[0,1]^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same $\sigma$-algebra. In this paper we…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that…
We overcome one of Bell's objections to `quantum measurement' by generalizing the definition to include systems outside the laboratory. According to this definition a {\sl generalized quantum measurement} takes place when the value of a…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov…
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…
Within the framework of constructions for quantifying entanglement, we build a natural scenario for the assembly of multipartite entanglement measures based on Hopf bundle-like mappings obtained through Clifford algebra representations.…
Gravity-induced quantum interference is a remarkable effect that has already been confirmed experimentally, and it is a phenomenon in which quantum mechanics and gravity play simultaneously an important role. Additionally, a generalized…
Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…
Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path) integrals by gauge theory or non-linear…
This pedagogical article solves an interesting problem in quantum measure theory. Although a quantum measure $\mu$ is a generalization of an ordinary probability measure, $\mu$ need not satisfy the usual additivity condition. Instead, $\mu$…