Related papers: Quantum tomography meets dynamical systems and bif…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We describe an approach for characterizing the process of quantum gates using quantum process tomography, by first modeling them in an extended Hilbert space, which includes non-qubit degrees of freedom. To prevent unphysical processes from…
Quantum state tomography is an important tool for quantum communication, computation, metrology, and simulation. Efficient quantum state tomography on a high dimensional quantum system is still a challenging problem. Here, we propose a…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…
We explore the intimate relationship between quantum lithography, Heisenberg-limited parameter estimation and the rate of dynamical evolution of quantum states. We show how both the enhanced accuracy in measurements and the increased…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider protocols based on geometry of platonic solids and other polyhedrons with high degree of symmetry such as…
Quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We develop the BFGS algorithm to study…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…