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 interactions. For all power-law exponents between and , where is the dimension of the system, the protocol yields a polynomial speed-up for and a superpolynomial speed-up for , compared to the state of the art. For all , 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.
Highlights
Harnessing entanglement between many particles is key to a quantum advantage in applications including sensing and timekeeping [1,2], secure communication [3], and quantum computing [4,5]
Encoding quantum information into a multiqubit Greenberger-HorneZeilinger-like (GHZ-like) state is desirable as a subroutine in many quantum applications, including metrology [2], quantum computing [6,7], anonymous quantum communication [8,9], and quantum secret sharing [10]
The speed at which one can unitarily encode an unknown qubit state aj0i þ bj1i into a GHZ-like state aj00...0i þ bj11...1i of a large system is constrained by LiebRobinson bounds [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] and depends on the nature of the interactions in the system
Summary
Harnessing entanglement between many particles is key to a quantum advantage in applications including sensing and timekeeping [1,2], secure communication [3], and quantum computing [4,5]. In systems with finite-range interactions and power-law interactions decaying with distance r as 1=rα for all α ≥ 2d þ 1, where d is the dimension of the system, the Lieb-Robinson bounds imply a linear light cone for the propagation of quantum information [23,25]. In such systems, the linear size of a GHZ-like state that can be prepared from. IV, where we establish the tightness of existing Lieb-Robinson bounds and discuss implications for other types of speed limits associated with quantum information propagation
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