Tomographic Characterization of Three-Qubit Pure States with Only Two-Qubit Detectors

A tomographic process for three-qubit pure states using only pairwise detections is presented.Comment: 3 pages; revtex4; v2: the focus on tomography was emphasized and the experimental procedure detailed; v3: the text was improved in clarity, some mistakes were correcte

Entanglement quantifiers, entanglement crossover and phase transitions

Entanglement has been widely used as a tool for the investigation of phase transitions (PTs). However, analysing several entanglement measures in the two-qubit context, we see that distinct entanglement quantifiers can indicate different orders for the same PT. Examples are given for different Hamiltonians. This leaves open the possibility of addressing different orders to the same PT if entanglement is used as an order parameter. Moving on to the multipartite context, we show necessary and sufficient conditions for a family of entanglement monotones to confirm quantum PTs

Are all maximally entangled states pure?

We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement, exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of monogamy of entanglement: we establish the \textit{polygamy of entanglement}, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system.Comment: 5 pages, 1 figure. Proof of theorem 3 corrected e new results concerning the asymptotic regime include

Are all maximally entangled states pure?

We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of the monogamy of entanglement: we establish the polygamy of entanglement, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factorized of any other system

Entanglement quantifiers, entanglement crossover and phase transitions

Entanglement has been widely used as a tool for the investigation of phase transitions (PTs). However, analysing several entanglement measures in the two-qubit context, we see that distinct entanglement quantifiers can indicate different orders for the same PT. Examples are given for different Hamiltonians. This leaves open the possibility of addressing different orders to the same PT if entanglement is used as an order parameter. Moving on to the multipartite context, we show necessary and sufficient conditions for a family of entanglement monotones to confirm quantum PTs

Geometrically induced singular behavior of entanglement

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.Comment: 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 fixe