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Journal of the Optical Society of America B

Deterministic remote state preparation with weight graph states in quantum networks

Zongyi Li, Yuzhen Wei, Yongcheng Li, Min Jiang

Published Dec 19, 2023• 0 citations
Publisher

Abstract

The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.

DOI
10.1364/josab.511462

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The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.
Measurement-based quantum computation (MBQC) relies on entangled graph states, yet existing remote state preparation (RSP) protocols prepare only separable states, requiring subsequent entangling gates on the remote server. Here, we introduce Remote Graph State Preparation (RGSP), a framework that prepares arbitrary graph states directly from a single high-dimensional photonic qudit. By encoding multiple qubits and their graph connectivity into the photon's structured phase profile, RGSP can reduce or, for small computations, completely eliminate the need for server-side entangling operations among qubits. We show that under a reasonable noise model the resulting state fidelity is independent of the graph topology. Under cumulative fiber phase drift, we demonstrate that this fidelity is significantly enhanced by a ``highest-weight-first'' mode reordering strategy. Finally, we show that RGSP enables reduced-SWAP universal blind quantum computing on arbitrary topologies, reducing qubit overhead e.g., for a six-qubit Quantum Fourier Transform from 420420420 RSP qubits with a standard brickwork topology to 484848 RSP qubits. These results establish RGSP as a resource-efficient, topology-invariant primitive for quantum-secured cloud computing.
In this paper, two efficient proposals are presented by using maximal slice states and orthogonal measurement basis to realize the joint remote state preparation (RSP) of two-qubit and three-qubit states, respectively. Furthermore, this kind of joint RSP schemes could be generalized to the case of arbitrary multi-qubit states, which can be transmitted from two senders to one receiver with the supervision of one manager. The successful probability of this joint RSP scheme is always equal to 100% in spite of that quantum channel is composed of non-maximally entangled states.
Quantum networks typically comprise quantum channels, repeaters, and end nodes. Remote state preparation (RSP) allows one end node to prepare the states of the other end nodes remotely. While quantum discord has recently been recognized as necessary for RSP, it does not guarantee the practical implementation of RSP in quantum networks surpasses any classical method. Herein, we theoretically introduce and experimentally study a quantum resource that we call the RSP capability. This resource validates all the static and dynamic elements required to enable genuine quantum networks where the RSP’s implementation can outperform any classical emulation of entanglement- and qubit-unitaries-free strategies, including the static resources of Einstein-Podolsky-Rosen pairs and the dynamic resources of quantum channels and repeaters. Our experiment measures the RSP capability to demonstrate the transition between classical and nonclassical RSP depending on the photon-pair qualities. It shows that quantum discord does not confirm a nonclassical RSP, but the RSP capability does. These results help reveal the quantum advantages that emerge when networking RSP is in play. The authors introduce and experimentally study a quantum resource called the remote state preparation capability. This resource validates all static and dynamic elements required to enable quantum networks where the implementation of remote state preparation can outperform any classical emulation of entanglement- and qubit-unitaries-free strategies.
Remote state preparation (RSP) is a technique to transmit quantum states with classical communication and previously shared entanglement. In this paper, we consider RSP in a multiparty setting. A simple yet nontrivial case is studied, where there is one sender and two receivers. We put forth a broadcasting method for developing multiparty RSP protocols. We show that this method can remotely prepare arbitrary states by consuming classical and quantum resources. For preparing highly entangled states, the proposed method achieves the lower bound for the amount of consumed resources asymptotically.
We present a general scheme for multiparty joint remote preparation of an arbitrary m -qudit state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The n senders share the information of the prepared state. The first sender performs POVM on his particles according to his knowledge of the original state, the other n − 1 senders perform m -particle projective measurement and the receiver can probabilistically reconstruct the original state by performing unitary operations on his particles according to the senders' measurement results. The scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m -qudit state via pure entangled quantum states. Moreover, it discusses the relationship between the coefficients of the pure entangled states and the success probability.
Our concern is to design some deterministic schemes for remotely preparing an arbitrary W -class state from one sender to one of a number of receivers. Compared with previous remote preparation schemes, the real receiver in our schemes is unknown to the sender. Firstly, by introducing a novel entanglement transformation the sender can deterministically prepare an arbitrary W -class state with complex spectra to one of two remote receivers via two four-particle GHZ states as the quantum channel. As for preparing a W -class state with real spectra, by constructing a general and useful measurement basis for the sender, another economical protocol can be designed with unit success probability. These schemes are extended to multiparties via two multi-particle GHZ states as the quantum channel. The classical communication costs of all the schemes are calculated to determine the classical resources required.