相关论文: A Topos Perspective on the Kochen-Specker Theorem:…
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a…
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…
Topos formalism for quantum mechanics is interpreted in a broader, information retrieval perspective. Contexts, its basic components, are treated as sources of information. Their interplay, called daseinisation, defined in purely logical…
Essential elements of quantum theory are derived from an epistemic point of view, i.e., the viewpoint that thetheory has to do with what can be said about nature. This gives a relationship to statistical reasoning and to other areas of…
In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other…
Based on the notion of a $\Delta$-group(oid), ring-valued invariants of pairs of topological spaces can be defined in intrinsic topological terms.
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented.
Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…
In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states which are free (because they can be…
The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This `coherence' is rigorously quantified by resource theories, which aim to understand how such properties may…
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space $\HH^n$ is presented. In particular new examples of $Sp(n)Sp(1)$-invariant translation invariant continuous valuations are…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This…
Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for…
The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a…
Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as…