Related papers: Continuous discretization of infinite dimensional …
The final version of a new approach to quantum theory is formulated in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to…
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
The relationship between discontinuous and continuous stochastic processes in Hilbert space is investigated. It is shown that for any continuos process there is a parent discontinuous process, that becomes the continuous one in the proper…
We argue about the following concepts:(i)introduction of endo and exo-observer of a physical system (ii) possible relation between endo, exo-observer and continuum/discrete nature of the same system (iii)the distinction about two categories…
In this Near Intermediate-Scale Quantum era, there are two types of near-term quantum devices available on cloud: superconducting quantum processing units (QPUs) based on the discrete variable model and linear optics (photonics) QPUs based…
This note contains the complete mathematical proof of the main Theorem of the paper "How continuous measurements in finite dimension are actually discrete" (quant-ph/0702068), thus showing that in finite dimension any measurement with…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
Measurements destroy entanglement. Building on ideas used to study `quantum disentangled liquids', we explore the use of this effect to characterize states of matter. We focus on systems with multiple components, such as charge and spin in…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling fulfilling quantum nondemolition…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
Distinguishability and, by extension, observability are key properties of dynamical systems. Establishing these properties is challenging, especially when no analytical model is available and they are to be inferred directly from…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We introduce the concept of fidelity for dynamical maps in an open quantum system scenario. We derive an inequality linking this quantity to the distinguishability of the inducing environmental states. Our inequality imposes constraints on…
It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…