Entanglement underlies all of quantum information science. It is most familiar as a relation between two parts of a single system, in which the properties of each part—taken separately—are uncertain but at the same time correlated with the properties of the other part. This so-called “bipartite entanglement” is, however, just one way in which a system can be entangled. Much more complicated is ...

At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of ent...

The physical concept of quantum entanglement state was applied to cooperative behavior of two ants (agents) pushing a pebble, which is too heavy for one ant, developed by Summhammer. His conventional study showed that the two quantum-inspired ants imitating quantum entanglement state can push the pebble up to twice relative to the two classical ants in independent relation. In order to set up a...

This paper identifies a formal connection between physical problems related to entanglement detection and complexity classes in theoretical computer science. In particular, we show that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), QSZK, and QIP), there corresponds a natural entanglement or correlation detection problem that is complete for that class. ...

The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that the classical-quantum correspondences such as encodings can be treated as diagonal (d-) entanglements. The mutual entropy of the d-compound and entangled states lead to two different types of entropies for a given quantum state: the von Neumann entropy, wh...

We explore entanglement in composite quantum systems and how its peculiar properties are exploited in quantum information and communication protocols by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for Bell states generation, measurem...

The concentration and distribution of quantum entanglement is an essential ingredient in emerging quantum information technologies. Much theoretical and experimental effort has been expended in understanding how to distribute entanglement in one-dimensional networks. However, as experimental techniques in quantum communication develop, protocols for multi-dimensional systems become essential. H...

We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric games and obtain a complete set of quantum Nash equilibria. Apart from those available with the maximal entanglement, these quantum Nash equilibria are exten...

Quantum entanglement in the Hénon–Heiles system is analyzed using the squeezed coherent state. Enhancement of quantum entanglement via squeezing is explored in connection with chaotic and regular dynamics of the system. It is found that the entanglement enhancement via squeezing is implicitly linked to the local structure of the classical phase-space and it shows a clear quantum-classical corre...

Quantum entanglement between photon pairs is fragile and can easily be masked by losses in transmission path and noise in the detection system. When observing the quantum entanglement between the spatial states of photon pairs produced by parametric down-conversion, the presence of an obstruction introduces losses that can mask the correlations associated with the entanglement. Here we show tha...