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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…
Using a recently introduced framework, we derive criteria for quantum k-separability, which are very easily computed. In the case k = 2, our criteria are equally strong to the best methods known so far, while in all other cases there are…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum_A w_A\,\rho_A'\otimes\rho_A''$, where $\rho_A'$ and $\rho_A''$ are density matrices for the two subsytems. In this Letter, it is…
Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum…
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…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An…
As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separablity [Phys. Rev. Lett. {\bf 127}, 060504 (2021)], we…
We derive criteria for $k$-separability of multipartite Quantum state
We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary…
In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum…
A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
The recent proposed realignment separability criterion for mixed is analyzed. We identify the essential part of this criterion is a swap operator followed by a partial transposition. Then we analyze the separability criterion of permutation…
In this paper, we present the necessary and sufficient conditions of separability for bipartite pure states in infinite dimensional Hilbert spaces. Let $M$ be the matrix of the amplitudes of $\ket\psi$, we prove $M$ is a compact operator.…
Separability from the spectrum is a significant and ongoing research topic in quantum entanglement. In this study, we investigate properties related to absolute separability from the spectrum in qudits-qudits states in the bipartite states…
The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of…
Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as…
We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are…
We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be…