Related papers: Cohomological framework for contextual quantum com…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
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…
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
The central notion in Connes' formulation of non commutative geometry is that of a spectral triple. Given a homogeneous space of a compact quantum group, restricting our attention to all spectral triples that are `well behaved' with respect…
Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…
Measurement-based quantum computation is a framework of quantum computation, where entanglement is used as a resource and local measurements on qubits are used to drive the computation. It originates from the one-way quantum computer of…
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum…
A scheme of universal quantum computation on a chain of qubits is described that does not require local control. All the required operations, an Ising-type interaction and spatially uniform simultaneous one-qubit gates, are…
We present a new framework for imaging and sensing based on utilizing a quantum computer to coherently process quantum information in an electromagnetic field. We describe the framework, its potential to provide improvements in imaging and…
An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
I relate contextuality to line bundles. Line bundles are important in algebraic geometry, they determine through their global sections rational maps to projective spaces. I explain how such maps, if they exist, relate rationally the input…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…