Quantum mechanics exhibits a wide range of non-classical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well-known that nonclassicality (e.g., squeezing, spin-squeezing, coherence) can be converted into entanglement. In this work, we present a general framework, based on superposition, for structurally connecting and converting non-classicality to entanglement. In addition to capturing the previously known results, this framework also allows us to uncover new entanglement convertibility theorems in two broad scenarios, one which is discrete and one which is continuous. In the discrete setting, the classical states can be any finite linearly independent set. For the continuous setting, the pertinent classical states are 'symmetric coherent states,' connected with symmetric representations of the group SU (K). These results generalize and link convertibility properties from the resource theory of coherence, spin coherent states, and optical coherent states, while also revealing important connections between local and non-local pictures of non-classicality.Quantum mechanics currently provides our deepest description of nature. Despite this, much of our everyday experience can be accurately captured within a classical description. What is special about the nonclassical states of a physical system, and what distinguishes them from the more commonplace classical states? Certainly, one of the most important manifestations of non-classicality is entanglement of multipartite systems. Schrödinger even viewed entanglement as "the characteristic trait of quantum mechanics" [1]. Yet there are situations where entanglement has no natural role in describing non-classicality, such as Fock states in optics [2]. Particularly for non-composite systems, other notions of non-classicality appear better suited for characterizing quantum states.A key aspect where quantum mechanics departs from classical mechanics is the prominence of the superposition principle. This elementary tenet of quantum theory supplies a very general framework for categorizing classical and non-classical states. Depending on the particular setting, we may specify some important subset of pure states {|c } c∈I to be the 'classical' pure states of the system. We can then directly associate non-classicality with superposition: a state |ψ is non-classical if and only if it is a non-trivial superposition of classical states. In fact, entanglement fits naturally within this superposition framework, by specifying factorized states as the classical states.One famous example of classical states is that of optical coherent states, {|α } α∈C [2][3][4]. A completely different example is found in the resource theories of coherence [5] or reference frames [6], where the classical states are some fixed orthonormal basis {|k } M k=0 . In both examples, there is no distinction of subsystems, and entanglement is not obviously relevant. Nevertheless, there are fundamental connections between these single-system c...

Abstract. Hypergraph states are multi-qubit states that form a subset of the locally maximally entangleable states and a generalization of the well-established notion of graph states. Mathematically, they can conveniently be described by a hypergraph that indicates a possible generation procedure of these states; alternatively, they can also be phrased in terms of a non-local stabilizer formalism. In this paper, we explore the entanglement properties and nonclassical features of hypergraph states. First, we identify the equivalence classes under local unitary transformations for up to four qubits, as well as important classes of five-and six-qubit states, and determine various entanglement properties of these classes. Second, we present general conditions under which the local unitary equivalence of hypergraph states can simply be decided by considering a finite set of transformations with a clear graph-theoretical interpretation. Finally, we consider the question whether hypergraph states and their correlations can be used to reveal contradictions with classical hidden variable theories. We demonstrate that various noncontextuality inequalities and Bell inequalities can be derived for hypergraph states.

We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and similar scenarios. This approach offers a straightforward scheme for experimental implementations of the tests via modular variable measurements. In addition to the continuous variable case, our condition can also be applied to finite-dimensional systems in discrete phase space, using Heisenberg-Weyl operators. This approach, therefore, offers a unified picture of contextuality with a geometric flavor.