Related papers: Entanglement transformations using separable opera…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…
Entanglement is one of the key feature of quantum world and any entanglement measure must satisfy some basic laws. Most important of them is the invariance of entanglement under local unitary operations. We show that this is no longer true…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…
Quantifying entanglement is one of the most important tasks in the entanglement theory. In this paper, we establish entanglement monotones in terms of an operational approach, which is closely connected with the state conversion from pure…
The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion…
This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum…
We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the…
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere…
We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.
It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…
A definition of the Schmidt number of a state of an infinite dimensional bipartite quantum system is given and properties of the corresponding family of Schmidt classes are considered. The existence of states with a given Schmidt number…
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
The entangling power of a bipartite unitary operation shows the maximum created entanglement with the product input states. For an arbitrary two-qubit unitary operation, it is sufficient to consider its normalized operation $U$ with…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
For a closed densely defined operator $T$ from a Hilbert space $\mathfrak{H}$ to a Hilbert space $\mathfrak{K}$, necessary and sufficient conditions are established for the factorization of $T$ with a bounded nonnegative operator $X$ on…
We present a general necessary and sufficient criterion for the possibility of a state transformation from one mixed Gaussian state to another of a bi-partite continuous-variable system with two modes. The class of operations that will be…
The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing…