Abstract
In some many-body systems, certain ground-state entanglement (Rényi) entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either or is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking) ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
- Received 19 March 2014
DOI:https://doi.org/10.1103/PhysRevX.4.041028
This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Popular Summary
Richard Feynman pioneered the notion of a universal quantum simulator: a device capable of processing quantum information that potentially supersedes any classical computer at simulating quantum systems. This idea embraces much of quantum information research and the technologies stemming from it and has motivated the goal of realizing such a device. However, quantifying to what extent a given quantum system can outperform a classical simulator is problematic. We investigate how a many-body system can operate as an efficient quantum simulator and the extent to which a quantum algorithm requires coherent manipulations. Our methodology relies on the local convertibility of the quantum system hosting the simulation. We demonstrate that the Majorana edge states establish genuinely quantum long-range correlations that may provide an additional resource for a given computational protocol.
We consider ground states with and without Majorana edge states, where Majorana fermions are a perplexing class of particles that are their own antiparticles. Our goal is to determine characteristics that a quantum computer must possess in order for it to exceed the computational properties of a classical computer. We isolate the entanglement generated by the edge states and show that it can decrease, while the entanglement of the bulk states increases, and vice versa. Since classical processes can never increase entanglement, this contrasting behavior signals the presence of genuine quantum properties. We understand the decrease of edge-state entanglement as a recombination effect and argue that the lack of local convertibility that it entails constitutes evidence for long-range entanglement.
We anticipate that studies of protected edge states and new quantum algorithms will be critical for future quantum machines.