Wigner's phase-space density

D. Iagolnitzer

H. J. Korsch, Michael Berry

Deepesh Khushwani, Priya Batra, V. R. Krithika +1 more

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 tomography in discrete Wigner phase space can also be implemented. We observe that for a certain class of states, such as harmonic states, the Wigner matrix is far more sparse compared to the density matrix in the computational basis. Additionally, reading only a small part of the Wigner matrix may suffice to infer certain behavior of quantum dynamics. In such cases, selective Wigner phase space tomography (SWPST) can be more efficient than the usual density matrix tomography (DMT). Employing nuclear magnetic resonance methods on a three-qubit nuclear spin register, we experimentally estimate Wigner matrices of various two-qubit quantum states. As a specific example application of SWPST, we study the evolution of spin coherent states under the quantum chaotic kicked top model and extract signatures of quantum-classical correspondence in the Wigner phase space.

M. Kira, S. W. Koch

H. J. Korsch

The quantum-mechanical joint (quasi-) density in phase space (the Wigner distribution) for thermodynamic equilibrium is studied in the semiclassical limit h(cross) to 0. The approximation is of an asymptotic (WKB) type and nonperturbative in character. The equilibrium phase-space distribution can be expressed in terms of classical paths satisfying certain well defined conditions. These paths are complex-valued, i.e. classically forbidden. The resulting semiclassical expression for the equilibrium Wigner phase-space density agrees with the exact quantum result for the analytical solvable case of harmonic potentials for all temperatures.

Jens Peder Dahl

The problem of two particles in a common harmonic oscillator potential interacting through harmonic oscillator forces is discussed in the Weyl–Wigner phase-space representation. The Wigner function of the system is an ordinary function of the phase-space constants of the motion. The density functional description of the system is touched upon. The functional that determines the confining harmonic potential from the particle density is also an ordinary function.