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The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by constructing a Schmidt number witness that detects it. We…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
We address the problem of completely characterizing multi-particle states including loss of information to unobserved degrees of freedom. In systems where non-classical interference plays a role, such as linear-optics quantum gates, such…
In this study, we enhance the understanding of entanglement transformations and their quantification by extending the concept of Schmidt vector from pure to mixed bipartite states, exploiting the lattice structure of majorization. The…
The amount of entanglement that exists in a parametric down-converted state is investigated in terms of all the degrees of freedom of the state. We quantify the amount of entanglement by the Schmidt number of the state, represented as a…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not…
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous…
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…
In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
A generic scheme for the parametrization of mixed state systems is introduced, which is then adapted to bipartite systems, especially to a 2-qubit system. Various features of 2-qubit entanglement are analyzed based on the scheme. Our…
We review two general criteria for deciding whether a pure bipartite quantum state describing a system of two identical particles is entangled or not. The first one considers the possibility of attributing a complete set of objective…
A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…
We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear combination of a mixed separable part and a pure…
The unambiguous detection and quantification of entanglement is a hot topic of scientific research, though it is limited to low dimensions or specific classes of states. Here we identify an additional class of quantum states, for which…
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…