Related papers: Schmidt number witnesses and bound entanglement
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…
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…
We prove a lower bound for Schmidt numbers of bipartite mixed states. This lower bound can be applied easily to low rank bipartite mixed states. From this lower bound it is known that generic low rank bipartite mixed states have relatively…
A deep understanding of quantum entanglement is vital for advancing quantum technologies. The strength of entanglement can be quantified by counting the degrees of freedom that are entangled, which results in a quantity called Schmidt…
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 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…
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…
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…
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…
The Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid…
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…
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…
An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.
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…
Entanglement plays a crucial role in quantum information science and many-body physics, yet quantifying it in mixed quantum many-body systems has remained a notoriously difficult problem. Here, we introduce families of quantitative…
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 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…
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…
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…
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…