Related papers: Continuous discretization of infinite dimensional …
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.…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
We develop spectral theorems for nonautonomous linear difference systems, considering different types of $\mu$-dichotomies, both uniform and nonuniform. In the nonuniform case, intriguing scenarios emerge -- that have been employed but…
Phase transitions represent a compelling tool for classical and quantum sensing applications. It has been demonstrated that quantum sensors can in principle saturate the Heisenberg scaling, the ultimate precision bound allowed by quantum…
In this paper, we establish a general theoretical framework for the description of continuous quantum measurements and the statistics of the results of such measurements. The framework concerns the measurement of an arbitrary quantum system…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
An arbitrarily dense discretisation of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the…
Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of high-dimensional entanglement can be simulated by using multiple…
Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of H\"older continuity; the second concerns contraction…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
Dynamics-based certification of quantumness is an approach to witnessing the nonclassical character of some continuous-variable states, under the assumption that their dynamics is known. Contrary to other tests of nonclassicality for single…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
In this paper, a linear infinite dimensional distributed systems in a Hilbert space has been discussed and analyzed where the dynamics of system is governed by strongly continuous semi-groups. The characterizations of regional strategic…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…