相关论文: Labels for non-individuals

A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $\mathbf{ZF}$ a new characterization of iso-dense spaces in terms of…

While the theory of labelled well-quasi-order has received significant attention in the graph setting, it has not yet been considered in the context of permutation patterns. We initiate this study here, and show how labelled well quasi…

In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…

The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…

We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum…

Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical…

In contrast to conventional, dynamical entanglement, in which particles with definite identity have uncertain properties, in so-called statistical entanglement, which arises between indistinguishable particles because of quantum symmetry…

A measurable relation algebra is a relation algebra in which the identity element is a sum of atoms that can be measured in the sense that the "size" of each such atom can be defined in an intuitive and reasonable way (within the framework…

Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…

We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…

Equations are ubiquitous in most mathematical activities. Nevertheless, in this paper it is shown how to do standard mathematics without any equation at all. More than that, it is proven there is a foundational framework for standard…

A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos…

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called…

Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in…

A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…

A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…

It is shown that the non-associative operators in a non-associative quantum theory are unobservables. The observable quantity may be presented only by the elements of some associative subalgebra. It is shown that the elements of the…

We introduce the task of anonymous metrology, in which a physical parameter of an object may be determined without revealing the object's location. Alice and Bob share a correlated quantum state, with which one of them probes the object.…