Related papers: High Schmidt number concentration in quantum bound…
Genuine high-dimensional entanglement, i.e. the property of having a high Schmidt number, constitutes a resource in quantum communication, overcoming limitations of low-dimensional systems. States with a positive partial transpose (PPT), on…
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…
A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter…
Entanglement is a central resource in quantum information science, yet its structure in high dimensions remains notoriously difficult to characterize. One of the few general results on high-dimensional entanglement is given by peel-off…
Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. Schmidt number is a quantity on the entanglement dimension of a bipartite state. Here we build families of k-positive maps from…
The Schmidt numbers quantify the entanglement degree of quantum states. Quantum states with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers.…
The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite…
We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on…
The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states…
Transmission of high dimensional entanglement through quantum channels is a significant area of interest in quantum information science. The certification of high dimensional entanglement is usually done through Schmidt numbers. Schmidt…
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…
The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation…
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…
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is…
We investigate the structure of $k$-positivity and Schmidt numbers for classes of linear maps and bipartite quantum states exhibiting symplectic group symmetries. Specifically, we consider (1) linear maps on $M_d(\mathbb{C})$ which are…
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…
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 introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local…