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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…
We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…
We present a class of entanglement identifiers which has the following experimentally friendly feature: once the expectation value of the identifier exceeds some definite limit, we can conclude the state is entangled, even if not all…
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…
Entanglement witnesses (EWs) are a versatile tool to detect entangled states and characterize related properties of entanglement in quantum information theory. A witness $W$ corresponds to an observable satisfying…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental…
We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have same entangling power is arrived. The relation also helps in finding the lower…
For any bipartite systems, a universal entanglement witness of rank-4 for pure states is obtained and a class of finite rank entanglement witnesses is constructed. In addition, a method of detecting entanglement of a state only by entries…
We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness…
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…
We develop a novel necessary condition of quantum correlation. It is utilized to construct $d$-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of $O(d)$ measurement outcomes compared to…
The generation and the characterization of multipartite entangled light is an important and challenging task in quantum optics. In this paper the entanglement properties of the light emitted from a planar semiconductor microcavity are…
It is shown that, every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide…
We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…
For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues $\lambda_k$ of $\rho$ and…
We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
We consider a two-spectra inverse problem for the one-dimensional Schr\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this…