相关论文: Tomographic map within the framework of star-produ…
We review the formalism of center-of-mass tomograms that allows us to describe quantum states in terms of probability distribution functions. We introduce the concept of separable and entangled probability distributions for the…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used.…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
Quantum tomography for continuous variables is based on the symplectic transformation group acting in the phase space. A particular case of symplectic tomography is optical tomography related to the action of a special orthogonal group. In…
We formulate the notion of quantum channels in the framework of quantum tomography and address there the issue of whether such maps can be regarded as classical stochastic maps. In particular kernels of maps acting on probability…
The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
Stochastic and bistochastic matrices providing positive maps for spin states (for qudits) are shown to form semigroups with dense intersection with the Lie groups $IGL(n, \mathbb{R})$ and $GL(n, \mathbb{R})$ respectively. The density matrix…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
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…
The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability…
In this note we classify invariant star products with quantum momentum maps on symplectic manifolds by means of an equivariant characteristic class taking values in the equivariant cohomology. We establish a bijection between the…
We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel…
We present a complete methodology for testing the performances of quantum tomography protocols. The theory is validated by several numerical examples and by the comparison with experimental results achieved with various protocols for whole…
We propose an approach to reconstruct any superconducting charge qubit state by using quantum state tomography. This procedure requires a series of measurements on a large enough number of identically prepared copies of the quantum system.…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.