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Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…

The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic…

Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a…

We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…

A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…

The familiar Greenberger-Horne-Zeilinger (GHZ) states can be rewritten by entangling the Bell states for two qubits with a state of the third qubit, which is dubbed entangled entanglement. We show that in this way we obtain all 8…

Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of…

A maximally entangled state is a quantum state which has maximum von Neumann entropy for each bipartition. Through proposing a new method to classify quantum states by using concurrences of pure states of a region, one can apply Bell's…

Quantum information science has profoundly changed the ways we understand, store, and process information. A major challenge in this field is to look for an efficient means for classifying quantum state. For instance, one may want to…

Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent…

All the states of N qubits can be classified into N-1 entanglement classes from 2-entangled to N-entangled (fully entangled) states. Each class of entangled states is characterized by an entanglement index that depends on the partition of…

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…

Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…

We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the…

Although entanglement is a basic resource for reaching quantum advantange in many computation and information protocols, we lack a universal recipe for detecting it, with analytical results obtained for low dimensional systems and few…

In this study, we introduce an autonomous method for addressing the detection and classification of quantum entanglement, a core element of quantum mechanics that has yet to be fully understood. We employ a multi-layer perceptron to…

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…

We build a machine learning model to detect correlations in a three-qubit system using a neural network trained in an unsupervised manner on randomly generated states. The network is forced to recognize separable states, and correlated…