Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems

Open Access

Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems

Minh C. Tran, Andrew Y. Guo, Abhinav Deshpande, Andrew Lucas, and Alexey V. Gorshkov

Phys. Rev. X 11, 031016 – Published 21 July 2021

Abstract

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law ( $1 / r^{α}$ ) interactions. For all power-law exponents $α$ between $d$ and $2 d + 1$ , where $d$ is the dimension of the system, the protocol yields a polynomial speed-up for $α > 2 d$ and a superpolynomial speed-up for $α \leq 2 d$ , compared to the state of the art. For all $α > d$ , the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. In addition, the protocol provides a lower bound on the gate count in digital simulations of power-law interacting systems.

Received 20 October 2020
Revised 8 April 2021
Accepted 25 May 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031016

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International 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

Physics Subject Headings (PhySH)

Entanglement manipulation Entanglement production Quantum state transfer

Quantum Information, Science & Technology

Authors & Affiliations

Minh C. Tran ^1,2, Andrew Y. Guo^1,2, Abhinav Deshpande ^1,2, Andrew Lucas^3,4, and Alexey V. Gorshkov ^1,2

¹Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
²Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
³Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
⁴Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA

Popular Summary

Particles in physical systems may interact with each other through long-range interactions, which typically decay with the distance between the particles. How fast the interactions decay with the distance defines whether the systems display local or nonlocal correlations—for example, particles may be entangled with only nearby (local) particles or with ones at a distance (nonlocal). We discover that a certain class of long-range interacting systems, which has been previously conjectured to be local, can actually display very nonlocal behavior.

In addition, we show that quantum information can propagate in these systems at a speed that saturates the upper limits imposed by quantum mechanics. Our work therefore disproves previous conjectures of tighter speed limits for these systems. It also rules out the possibility of generalizing several theoretical analyses that rely on the existence of such conjectured limits to these systems.

Practically, we significantly advance the state of the art in transferring quantum information and preparing multiparticle entangled states, thus enabling improvements in many quantum applications such as metrology, quantum computing, anonymous quantum communication (in which an eavesdropper cannot infer information shared among parties), and quantum secret sharing (in which a secret shared among several parties is revealed only when all of them use their keys collectively).

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