Related papers: Maximally Entangled States
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
Strong numerical evidence is presented suggesting that all two-qubit mixed states are equivalent to X states by a single entanglement-preserving unitary (EPU) transformation, so that the concurrence of such an X state equals that of the…
We investigate the inseparability of states generated by superposition of a multipartite pure entangled state with a product state. In particular, we identify specific multipartite entangled states that will always produce inseparability…
Fully entangled fraction is a definition for bipartite states, which is tightly related to bipartite maximally entangled states, and has clear experimental and theoretical significance. In this work, we generalize it to multipartite case,…
Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the…
The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…
We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…
The infinite projected entangled pair states (iPEPS) technique [J. Jordan {\it et al.}, Phys. Rev. Lett. {\bf 101}, 250602 (2008)] has been widely used in the recent years to assess the properties of two-dimensional quantum systems, working…
We investigate the extent to which two particles can be maximally entangled when they are also similarly entangled with other particles on a complete graph, focusing on Werner, isotropic, and Brauer states. To address this, we formulate and…
The Bell's basis is composed of four maximally entangled states of two qubits, named Bell states. They are usual tools in many theoretical studies and experiments. The aim of this paper is to find out the symmetries that determine a Bell…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…
We present an revised geometric measure of entanglement (RGME). The revised version is an entanglement monotone. Some useful inequalities about RGME are deduced. For exemplification, we give the formulas of RGME for the two-parameter class…
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the…
In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value…
We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in…
It is known that probabilistically mixing an arbitrary pair of pure quantum states, one of which is entangled and the other product, in any bipartite quantum system, one always obtains an entangled state, provided the entangled state of the…
Currently the entanglement of formation can be calculated analytically for mixed states in a $(2\otimes2)$-dimensional Hilbert space. For states in higher dimensional Hilbert space a closed formula for quantifying entanglement does not…