Topological entanglement far and wide

Zlatko Papić, Bogdan Andrei Bernevig, Nicolas Regnault

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the excitations of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.

Sead Spuzic

Wei Kang Zhu, Shou-Shu Gong, F. D. M. Haldane +1 more

Topological quantum states with non-Abelian Fibonacci anyonic excitations are widely sought after for the exotic fundamental physics they would exhibit, and for universal quantum computing applications. The fractional quantum Hall (FQH) state at a filling factor of ν=12/5 is a promising candidate; however, its precise nature is still under debate and no consensus has been achieved so far. Here, we investigate the nature of the FQH ν=13/5 state and its particle-hole conjugate state at 12/5 with the Coulomb interaction, and we address the issue of possible competing states. Based on a large-scale density-matrix renormalization group calculation in spherical geometry, we present evidence that the essential physics of the Coulomb ground state (GS) at ν=13/5 and 12/5 is captured by the k=3 parafermion Read-Rezayi state (RR_{3}), including a robust excitation gap and the topological fingerprint from the entanglement spectrum and topological entanglement entropy. Furthermore, by considering the infinite-cylinder geometry (topologically equivalent to torus geometry), we expose the non-Abelian GS sector corresponding to a Fibonacci anyonic quasiparticle, which serves as a signature of the RR_{3} state at 13/5 and 12/5 filling numbers.

Dmitry Melnikov

Dong Zhou, Robert Joynt

Haapasalo Erkka, Kraft Tristan, Juha-Pekka Pellonpää +1 more

Recently, various nonclassical properties of quantum states and channels have been characterized through an advantage they provide in quantum information tasks over their classical counterparts.Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks.So far, these characterizations have been established only in the finite-dimensional setting, hence, leaving out central resources in continuous variable systems such as entanglement and nonclassicality of states as well as entanglement breaking and broadcasting channels.In this Letter, we present a fully general framework for resource quantification in infinite-dimensional systems.The framework is applicable to a wide range of resources with the only premises being that classical randomness cannot create a resource and that the resourceless objects form a closed set in an appropriate sense.As the latter may be hard to establish for the abstract topologies of continuous variable systems, we provide a relaxation of the condition with no reference to topology.This envelopes the aforementioned resources and various others, hence, giving them an interpretation as performance enhancement in so-called input-output games.