# Topological squashed entanglement: Nonlocal order parameter for one-dimensional topological superconductors

@article{Maiellaro2022TopologicalSE, title={Topological squashed entanglement: Nonlocal order parameter for one-dimensional topological superconductors}, author={Alfonso Maiellaro and Antonio Di Marino and Fabrizio Illuminati}, journal={Physical Review Research}, year={2022} }

Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two decades. Here we show that the end-to-end, long-distance, bipartite squashed entanglement between the edges of a many-body system, deﬁned in terms of the edge-to-edge quantum conditional mutual information, is the natural nonlocal order parameter for topological…

## 2 Citations

### Squashed entanglement in one-dimensional quantum matter

- Physics
- 2022

We introduce the concept of squashed entanglement between a system edges in one-dimensional quantum matter. We show that edge squashed entanglement discriminates unambiguously between topological…

### Edge states, Majorana fermions, and topological order in superconducting wires with generalized boundary conditions

- PhysicsPhysical Review B
- 2022

We study the properties of one-dimensional topological superconductors under the inﬂuence of generic boundary conditions mimicking the coupling with external environments. We identify a general…

## References

SHOWING 1-10 OF 125 REFERENCES

### Entanglement topological invariants for one-dimensional topological superconductors

- PhysicsPhysical Review B
- 2020

Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for…

### Topological Phases of One-Dimensional Fermions: An Entanglement Point of View

- Physics
- 2011

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional…

### Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

- Physics
- 2020

We study the disconnected entanglement entropy, $S^D$, of the Su-Schrieffer-Heeger model. $S^D$ is a combination of both connected and disconnected bipartite entanglement entropies that removes all…

### Experimental observation of classical analogy of topological entanglement entropy

- Physics, Materials ScienceNature Communications
- 2019

A scheme to observe topological entanglement entropy in the topological order by constructing specific minimum entropy states (MESs) and experimentally construct classical analogs of minimum entropyStates to simulate nontrivial topological orders by observing the TEE in Kitaev toric code is proposed.

### Long-distance entanglement in many-body atomic and optical systems

- Physics
- 2009

We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body…

### Majorana fermions and multiple topological phase transition in Kitaev ladder topological superconductors

- Physics
- 2014

Motivated by the InSb nanowire superconductor system, we investigate a system where one-dimensional topological superconductors are placed in parallel. It would be simulated well by a ladder of the…

### Topological entanglement entropy.

- PhysicsPhysical review letters
- 2006

The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity.

### Topological phases, Majorana modes and quench dynamics in a spin ladder system

- Physics
- 2011

We explore the salient features of the ‘Kitaev ladder’, a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave…

### The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors

- Mathematics
- 2016

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological…