Related papers: Absolute Schmidt number: characterization, detecti…
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…
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…
Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems.…
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…
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 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…
Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any…
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…
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…
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…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.…
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…
Schmidt decomposition is a powerful tool in quantum information. While Schmidt decomposition is universal for bipartite states, its not for multipartite states. In this article, we review properties of bipartite Schmidt decompositions and…
The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under…
High-dimensional entanglement, captured by the Schmidt number, underpins advantages in quantum information tasks, yet a unified resource-theoretic description across different Buscemi-type operational objects has been missing. Here we…
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…
The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which…
The dimensionality of entanglement is a core tenet of quantum information processing, especially quantum communication and computation. While it is natural to think of this dimensionality in finite dimensional systems, many of the…
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…