Non-negative Wigner functions for orbital angular momentum states
arXiv:0909.1887 · doi:10.1103/PhysRevA.81.012101
Abstract
The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.
4 pages. Minor changes (including title). To appear in Physica. Review A
References in corpus (9)
- Hudson's Theorem for finite-dimensional quantum systems
- Quantum Mechanics in Phase Space
- Classicality in discrete Wigner functions
- Non-negative Wigner functions in prime dimensions
- Extending Hudson's theorem to mixed quantum states
- Experimental test of uncertainty relations for quantum mechanics on a circle
- Minimum uncertainty measurements of angle and angular momentum
- Full quantum reconstruction of vortex states
- Interference in discrete Wigner functions
Cited by in corpus (12)
- Orbital angular momentum in phase space
- Wigner distribution of twisted photons
- Wigner function for a particle in an infinite lattice
- Angular performance measure for tighter uncertainty relations
- Clifford operations and homological codes for rotors and oscillators
- Orbital angular momentum from marginals of quadrature distributions
- Wigner representation of the rotational dynamics of rigid tops
- Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems
- Wigner distribution on a double cylinder phase space for studying quantum error correction protocol
- Normalizer Circuits and Quantum Computation
- Classical analogy of a cat state using vortex light
- Integral Quantization for the Discrete Cylinder