"Is entanglement monogamous?" asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett's legacy on quantum information theory. While the answer is affirmative in the qualitative sense, the situation is less clear if monogamy is intended as a quantitative limitation on the distribution of bipartite entanglement in a multipartite system, given some particular measure of entanglement. Here, we formalize what it takes for a bipartite measure of entanglement to obey a general quantitative monogamy relation on all quantum states. We then prove that an important class of entanglement measures fail to be monogamous in this general sense of the term, with monogamy violations becoming generic with increasing dimension. In particular, we show that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entanglement structure of the fully antisymmetric state in arbitrary dimension. Nevertheless, monogamy of such entanglement measures can be recovered if one allows for dimension-dependent relations, as we show explicitly with relevant examples.Introduction. Entanglement is a quintessential manifestation of quantum mechanics [1,2]. The study of entanglement and its distribution reveals fundamental insights into the nature of quantum correlations [3], on the properties of manybody systems [4,5], and on possibilities and limitations for quantum-enhanced technologies [6]. A particularly interesting feature of entanglement is known as monogamy [7], that is, the impossibility of sharing entanglement unconditionally across many subsystems of a composite quantum system.In the clearest manifestation of monogamy, if two parties A and B with the same (finite) Hilbert space dimension are maximally entangled, then their state is a pure state |Φ AB [8], and neither of them can share any correlation-let alone entanglement-with a third party C, as the only physically allowed pure states of the tripartite system ABC are product states |Φ AB ⊗ |Ψ C . Consider now the more realistic case of A and B being in a mixed, partially entangled state ρ AB . It is then conceivable for more parties to get a share of such entanglement. Namely, a state ρ AB on a Hilbert space H A ⊗ H B is termed "n-shareable" with respect to subsystem B if it admits a symmetric n-extension, i.e. a state ρ AB 1 ...B n on H A ⊗ H ⊗n B invariant under permutations of the subsystems B 1 , . . . , B n and such that the marginal state of A and any B j amounts to ρ AB . While even an entangled state can be shareable up to some number of extensions, a seminal result is that a state ρ AB is n-shareable for all n 2 if and only if it is separable, that is, no entangled state can be infinitely-shareable [7,[9][10][11][12]. This statement formalizes exactly the monogamy of entanglement (in an asymptotic setting), and has many important implications, including the equivalence between asymptotic quantum cloning and state e...

We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous classes of designs. We show that mutually orthogonal quantum Latin arrangements can be entangled in the same way than quantum states are entangled. Furthermore, we show that such designs naturally define a remarkable class of genuinely multipartite highly entangled states called k-uniform, i.e. multipartite pure states such that every reduction to k parties is maximally mixed. We derive infinitely many classes of mutually orthogonal quantum Latin arrangements and quantum orthogonal arrays having an arbitrary large number of columns. The corresponding multipartite k-uniform states exhibit a high persistency of entanglement, which makes them ideal candidates to develop multipartite quantum information protocols.

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We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schrödinger operator.

We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular, we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.