How can one prove that a given quantum state is entangled? In this paper we review
different methods that have been proposed for entanglement detection. We first explain the …

In information processing, as in physics, our classical world view provides an incomplete
approximation to an underlying quantum reality. Quantum effects like interference and …

We provide necessary and sufficient conditions for separability of mixed states of n-particle
systems. The conditions are formulated in terms of maps which are positive on product …

Invertible local transformations of a multipartite system are used to define equivalence
classes in the set of entangled states. This classification concerns the entanglement …

Quantum information theory is a branch of science at the frontier of physics, mathematics,
and information science, and offers a variety of solutions that are impossible using classical …

Consider three qubits A, B, and C which may be entangled with each other. We show that
there is a trade-off between A's entanglement with B and its entanglement with C. This …

Ho** to simplify the classification of pure entangled states of multi (m)− partite quantum
systems, we study exactly and asymptotically (in n) reversible transformations among n th …

Tensor network methods are taking a central role in modern quantum physics and beyond.
They can provide an efficient approximation to certain classes of quantum states, and the …

The theory of quantum information, that is, of the transmission, storage, and processing of
information using quantum-mechanical systems, is now well developed. It has been …

We present a review of theoretical and experimental aspects of multiphoton quantum optics.
Multiphoton processes occur and are important for many aspects of matter–radiation …