Related papers: Interference in discrete Wigner functions
We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result…
The cat state is shown to `store' a single photon through the superposition of its orthogonal counterpart with itself, and an excited oscillator state. Photon addition leads to a $\pi $ phase shift at origin in the observed phase space…
Quantum superpositions of distinct coherent states in a single-mode harmonic oscillator, known as "cat states", have been an elegant demonstration of Schrodinger's famous cat paradox. Here, we realize a two-mode cat state of electromagnetic…
We study the evolution of the hybrid entangled squeezed states of the qubit-oscillator system in the strong coupling domain. Following the adiabatic approximation we obtain the reduced density matrices of the qubit and the oscillator…
In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations within hybrid quantum systems. Specifically,…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
According to a classical result due to Hudson, the Wigner function of a pure, continuous variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum…
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…
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the…
The negativity of the discrete Wigner functions (DWFs) is a measure of non-classicality and is often used to quantify the degree of quantum coherence in a system. The study of Wigner negativity and its evolution under different quantum…
We have studied statistical properties of the values of the Wigner function W(x) of 1D quantum maps on compact 2D phase space of finite area V. For this purpose we have defined a Wigner function probability distribution P(w) = (1/V) int…
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…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schr\"odinger cat states, defined as orthonormalized eigenstates of…
In the framework of the spatial coherence wavelets, different features of the first-order spatial coherence (Young's interference) are analysed by calculating the corresponding marginal power spectrum, a close related quantity to the…
Time reversal and spin flip are discrete symmetry operations of substantial import to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of…
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial…
Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can…
We study numerically the dynamics of excitons on discrete rings in the presence of static disorder. Based on continuous-time quantum walks we compute the time evolution of the Wigner function (WF) both for pure diagonal (site) disorder, as…
We describe the symmetry group of the stabilizer polytope for any number $n$ of systems and any prime local dimension $d$. In the qubit case, the symmetry group coincides with the linear and anti-linear Clifford operations. In the case of…