Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

The Markov gap for geometric reflected entropy

The reflected entropy SR(A : B) of a density matrix ρAB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N2 gap between SR and I. We provide an information-theoretic interpretation of this gap by observing that SR− I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity SR− I the Markov gap. We then prove that for time-symmetric states in pure AdS3 gravity, the Markov gap is universally lower bounded by log(2)ℓAdS/2GN times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling SR− I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

Heterogeneity-stabilized homogeneous states in driven media

Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.

The Problem of the Non-Uniqueness of the Solution to the Inverse Problem of Recovering the Symmetric States of a Bistable Medium with Data on the Position of an Autowave Front

The paper considers the question of the possibility of recovering symmetric stable states of a bistable medium in the inverse problem for a nonlinear singularly perturbed autowave equation by data given on the position of an autowave front propagating through it. It is shown that under certain conditions, this statement of the problem is ill-posed in the sense of the non-uniqueness of the solution. A regularizing approach to its solution was proposed.

Omnipresence of Weak Antilocalization (WAL) in Bi2Se3 Thin Films: A Review on Its Origin

Topological insulators are materials with time-reversal symmetric states of matter in which an insulating bulk is surrounded by protected Dirac-like edge or surface states. Among topological insulators, Bi2Se3 has attracted special attention due to its simple surface band structure and its relatively large band gap that should enhance the contribution of its surface to transport, which is usually masked by the appearance of defects. In order to avoid this difficulty, several features characteristic of topological insulators in the quantum regime, such as the weak-antilocalization effect, can be explored through magnetotransport experiments carried out on thin films of this material. Here, we review the existing literature on the magnetotransport properties of Bi2Se3 thin films, paying thorough attention to the weak-antilocalization effect, which is omnipresent no matter the film quality. We carefully follow the different situations found in reported experiments, from the most ideal situations, with a strong surface contribution, towards more realistic cases where the bulk contribution dominates. We have compared the transport data found in literature to shed light on the intrinsic properties of Bi2Se3, finding a clear relationship between the mobility and the phase coherence length of the films that could trigger further experiments on transport in topological systems.