Related papers: On properties of Schmidt Decomposition
For many completely positive maps repeated compositions will eventually become entanglement breaking. To quantify this behaviour we develop a technique based on the Schmidt number: If a completely positive map breaks the entanglement with…
Now, the known ensembles of orthogonal states which are distinguishable by local operators and classical communication (LOCC) satisfy the condition that the sum of Schmidit numbers of the orthogonal states is not bigger than the dimensions…
In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational…
Bipartite quantum states with higher Schmidt numbers have been shown to outperform those with lower Schmidt numbers in various quantum information processing tasks, highlighting the operational advantage of entanglement dimensionality.…
Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
We consider the compact convex set of all bi-partite states of Schmidt number less than or equal to $k$, together with that of $k$-blockpositive matrices of trace one, which play the roles of Schmidt number witnesses. In this note, we look…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled…
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to…
The decompositions of separable Werner state, and also isotropic state, are well-known tough issues in quantum information theory, in this work we investigate them in the Bloch vector representation, exploring the symmetric informationally…
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods…
Recent progress in quantum optics has led to setups that are able to prepare high-dimensional quantum states for quantum information processing tasks. As such, it is of importance to benchmark the states generated by these setups in terms…
We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to…
We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation…
Can vectors with low Schmidt rank form mutually unbiased bases? Can vectors with high Schmidt rank form positive under partial transpose states? In this work, we address these questions by presenting several new results related to Schmidt…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
Understanding the nature of multipartite entanglement is a central mission of quantum information theory. To this end, we investigate the question of tripartite entanglement convertibility. We find that there exists no easy criterion to…
The ability to efficiently characterize the spatial correlations of entangled states of light is critical for applications of many quantum technologies such as quantum imaging. Here, we demonstrate highly efficient theoretical and…