Related papers: Simplifying Schmidt number witnesses via higher-di…
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…
The general class of Gaussian Schmidt-number witness operators for bipartite systems is studied. It is shown that any member of this class is reducible to a convex combination of two types of Gaussian operators using local operations and…
Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically…
We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness…
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…
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…
Witness operators are a central tool to detect entanglement or to distinguish among the different entanglement classes of multiparticle systems, which can be defined using stochastic local operations and classical communication (SLOCC). We…
We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments…
We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the…
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…
Absolutely separable states form a special subset of the set of all separable states, as they remain separable under any global unitary transformation unlike other separable states. In this work we consider the set of absolutely separable…
The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of…
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…
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…
We address the problem of optimising entanglement witnesses when a limited fixed set of local measurements can be performed on a bipartite system, thus providing a procedure, feasible also for experiments, to detect entangled states using…
In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled…
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…
Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt…
An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the…