Geometrically induced singular behavior of entanglement

TL;DR

This paper demonstrates that the geometry of quantum state spaces causes singularities in entanglement dynamics, supported by experimental photonic data and connections to condensed matter singularities.

Contribution

It reveals the geometric origin of entanglement singularities and experimentally verifies this phenomenon in photonic systems.

Findings

Singular points at the border of unentangled states cause entanglement singularities.

Experimental evidence from photonic parametric down conversion supports the theory.

Links established between entanglement singularities and condensed matter phenomena.

Abstract

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.