Related papers: Compatibility of subsystem states and convex geome…

This short note describes a method to tackle the (bipartite) quantum separability problem. The method can be used for solving the separability problem in an experimental setting as well as in the purely mathematical setting. The idea is to…

We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional…

Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state…

We consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness. Based on the properties of entanglement witness, we…

Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…

We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some…

We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…

In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…

The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.

Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum…

In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…

Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…

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…

The complete reducibility property for bipartite states reduced the separability problem to a proper subset of positive under partial transpose states and was used to prove several theorems inside and outside entanglement theory. So far…

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…

Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived…

Linear and nonlinear entanglement witnesses for a given bipartite quantum systems are constructed. Using single particle feasible region, a way of constructing effective entanglement witnesses for bipartite systems is provided by exact…

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss…

Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…