Related papers: Schmidt Decomposition of Multipartite 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…
Our previous work about algebraic-geometric invariants of the mixed states are extended and a stronger separability criterion is given. We also show that the Schmidt number of pure states in bipartite quantum systems, a classical concept,…
It is shown that for each mixed state there exists a Schmidt (super state vector) decomposition in terms of Hermitian operators. Its utilization for finding all twins is illustrated in full detail in the case of the two…
Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in the light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition. MME states are a special kind of…
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this…
In this note we generalize Nielsen's marjoization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83}, 436(1999)] to a special class of multipartite pure states which have generalized Schmidt…
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 this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
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 derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in Von Neumann entropy to…
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…
In this contribution we present a concise introduction to quantum entanglement in multipartite systems. After a brief comparison between bipartite systems and the simplest non-trivial multipartite scenario involving three parties, we review…
Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite…
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
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…