We show that $s$ waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of $s$ waves which allows us to perform the calculations analytically. This class includes a Gaussian, a maximally entangled as well as a ``shell'' state.We show that $s$ waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of $s$ waves which allows us to perform the calculations analytically. This class includes a Gaussian, a maximally entangled as well as a ``shell'' state.

Physical Review AOct 23, 200658 citations

The negativity of partial transpose versus the negativity of Wigner function

Mustapha Ziane, Fatima-Zahra Siyouri, M. El Baz +1 more

We investigate the multipartite entanglement in the phase space using the negativity of Wigner function (NWF) and in the Hilbert space using the negativity of partial transpose (NPT). We analyze comparatively these quantities and the different types of entanglements that are present in two major classes — GHZ and [Formula: see text] — made of coherent states. We show that the negativity of Wigner function can be used as a good measure of genuine entanglement in multipartite systems. However, the negativity of partial transpose is a good quantifier for only the bipartite entanglement in tripartite systems.We investigate the multipartite entanglement in the phase space using the negativity of Wigner function (NWF) and in the Hilbert space using the negativity of partial transpose (NPT). We analyze comparatively these quantities and the different types of entanglements that are present in two major classes — GHZ and [Formula: see text] — made of coherent states. We show that the negativity of Wigner function can be used as a good measure of genuine entanglement in multipartite systems. However, the negativity of partial transpose is a good quantifier for only the bipartite entanglement in tripartite systems.

International Journal of Geometric Methods in Modern PhysicsApr 3, 20193 citations

We show that

s

waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of

s

waves which allows us to perform the calculations analytically. This class includes a Gaussian, a maximally entangled as well as a ``shell'' state.