Related papers: Discrete phase-space structures and Wigner functio…
In this letter, the number-phase entropic uncertainty relation and the number-phase Wigner function of generalized coherent states associated to a few solvable quantum systems with nondegenerate spectra are studied. We also investigate time…
For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
Wigner functions help visualise quantum states and dynamics while supporting quantitative analysis in quantum information. In the discrete setting, many inequivalent constructions coexist for each Hilbert-space dimension. This fragmentation…
Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
In contrast to abstract statistical analyses in the literature, we present a concrete physical diagrammatic model of entanglement characterization and measure with its underlying discrete phase-space physics. This paper serves as a…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…
The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…
The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ to endow it with proper geometrical properties. We analyze the…
We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…
Both classical and quantum damped systems give rise to complex spectra and corresponding resonant states. We investigate how resonant states, which do not belong to the Hilbert space, fit the phase space formulation of quantum mechanics. It…
In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be…
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the…
A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations…
We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…
Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit -- quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analysed.…
We consider the phase space for a system of $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$ points and use the finite field $GF(d^{n})$ to label the corresponding axes. The…