相关论文: Topos Theoretical Reference Frames on the Category…

In this paper, we present a simple yet effective Boolean map based representation that exploits connectivity cues for visual tracking. We describe a target object with histogram of oriented gradients and raw color features, of which each…

Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…

Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…

Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…

We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between…

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…

Macroscopic quantum phenomena refer to quantum features in objects of `large' sizes, systems with many components or degrees of freedom, organized in ways where they can be identified as macroscopic objects. This emerging field is ushered…

Using the quantum two-body system as a familiar model, this talk will describe how entanglement can be used to select preferred observables for interrogating a physical system. The symmetries and dynamics of the quantum two-body system…

In statistics cumulants are defined to be functions that measure the linear independence of random variables. In the non-communicative case the Boolean cumulants can be described as functions that measure deviation of a map between algebras…

Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a…

The perspective-neutral formulation of quantum reference frames (QRFs) treats observers as quantum systems and describes physics relationally from within the composite system. While frame-change maps and frame-invariant resource sums are…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…

Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration…

Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…

The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…

Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…

We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory,…

Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…