Geometrically induced singular behavior of entanglement
arXiv:0709.0301 · doi:10.1103/PhysRevA.78.012318
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.
v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixed
References in corpus (25)
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Scaling of Entanglement close to a Quantum Phase Transitions
- Entanglement in a simple quantum phase transition
- On the volume of the set of mixed entangled states
- Bell Inequalities and the Separability Criterion
- Optimization of entanglement witnesses
- Robustness of entanglement
- Information-theoretic aspects of quantum inseparability of mixed states
- Witnessing multipartite entanglement
- The entanglement cost under operations preserving the positivity of partial transpose
- Quantifying Entanglement with Witness Operators
- Quantitative entanglement witnesses
- Experimental Detection of Entanglement with Polarized Photons
- Estimating entanglement measures in experiments
- Studying quantum spin systems through entanglement estimators
- Experimental detection of entanglement via witness operators and local measurements
- Electron Entanglement via a Quantum Dot
- Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
- When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
- Binegativity and geometry of entangled states in two qubits
- Witnessed Entanglement
- Entanglement versus energy in the entanglement transfer problem
- Enhancement of pairwise entanglement from $\mathbbm{Z}_2$ symmetry breaking
- Estimating entanglement of unknown states