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Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for…
Multipartite entanglement is an indispensable resource in quantum communication and computation, however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work, we study the…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a…
We show that any measure of entanglement that on pure bipartite states is given by a strictly concave function of the reduced density matrix is monogamous on pure tripartite states. This includes the important class of bipartite measures of…
We analyze form the topological perspective the space of all SLOCC (Stochastic Local Operations with Classical Communication) classes of pure states for composite quantum systems. We do it for both distinguishable and indistinguishable…
The contextual fraction introduced by Abramsky and Brandenburger defines a quantitative measure of contextuality associated with empirical models, i.e. tables of probabilities of measurement outcomes in experimental scenarios. In this paper…
We study the dynamics of the entanglement in one dimensional critical quantum systems after a local quench in which two independently thermalized semi-infinite halves are joined to form a homogeneous infinite system and left to evolve…
We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. We show that such a convergence is defined by the convergence to $0$ on the positive cone. Some results on unbounded…
The main concern of this paper is how to define proper measures of multipartite entanglement for mixed quantum states. Since the structure of partial separability and multipartite entanglement is getting complicated if the number of…
We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory,…
We prove that the relative entropy of entanglement is additive when \emph{at least one of the two states} belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal,…
We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using…
One of the fundamental traits of quantum entanglement is the restricted shareability among multipartite quantum systems, namely monogamy of entanglement, while it is well known that monogamy inequalities are always satisfied by entanglement…
We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group…
A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for…
We calculate the entanglement entropy of a slab of finite width in the pure Maxwell theory. We find that a large part of entropy is contributed by the entanglement of a mode, nonlocal in terms of the transverse magnetic field degrees of…
Measures of entanglement can be employed for the analysis of numerous quantum information protocols. Due to computational convenience, logarithmic negativity is often the choice in the case of continuous variable systems. In this work, we…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In…