Related papers: Dimensions, lengths and separability in finite-dim…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
Symmetry plays an important role in the field of quantum mechanics. In this paper, we consider a subclass of symmetric quantum states in the multipartite system $N^{\otimes d}$, namely, the completely symmetric states, which are invariant…
We show that, in finite dimensions, around any $m$-partite product state $\rho_{\rm prod}=\rho_1\otimes...\otimes\rho_m$, there exists an ellipsoid of separable states centered around $\rho_{\rm prod}$. This separable ellipsoid contains the…
One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial…
In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…
This note deals with estimating the volume of the set of separable mixed quantum states when the dimension of the state space grows to infinity. This has been studied recently for qubits; here we consider larger particles and conclude that,…
We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}.…
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem and characterize the set of effectively…
We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…
A finite dimensional quantum mechanical system is modeled by a density rho, a trace one, positive semi-definite matrix on a suitable tensor product space H[N] . For the system to demonstrate experimentally certain non-classical behavior,…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state…
A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…
We investigate separability and entanglement of mixed states in ${\cal C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
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 present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
We show that around any $m$-partite product state $\rho_{\rm prod}=\rho_1\otimes...\otimes\rho_m$ of full rank (that is ${\rm det}(\rho_{\rm prod})\neq 0)$, there exists a finite-sized closed ball of separable states centered around…
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…