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arXiv:quant-ph/9803056

Quantum repeaters for communication

H. J. Briegel, Wolfgang Dür, J. I. Cirac, Zoller, P.

Published Mar 20, 1998• 26 citations
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Abstract

In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. The scheme tolerates general errors on the percent level.

DOI
10.48550/arxiv.quant-ph/9803056

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In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. The scheme tolerates general errors on the percent level.
In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. Our scheme tolerates general errors on the percent level, it works with a polynomial overhead in time and a logarithmic overhead in the number of particles that need to be controlled locally.
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
Recently, Briegel et al. present a quantum repeaters protocol using nest entanglement purification for long distance quantum communication(Physical Review Letters \textbf{81},5932). In this paper we present a modified scheme for constructing an optimal quantum repeater using doubly entangled photon pairs that overcomes the limitations of quantum communication via noisy channels. Based on the imperfect quantum operations and classical communications, the polarization entangled quantum channels can be built with a better efficiency.
We discuss a long-distance quantum communication system based on entangled photon pairs, which apply entanglement as its fundamental resource. For distances longer than the coherence length of a counterpart noisy quantum channel, the fidelity of transmission is ordinarily so low that standard purification processes are not applicable. The quantum repeater stretches the length of the entangled photon pairs. And the high fidelity entanglement of photons between sender and receiver is obtained by entanglement purification and entanglement swapping. We compare the nested repeater with the common repeater and show that it outperforms the latter, which is built an EPR pair in less time.
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Quantum communication is a groundbreaking technology that is driving the future of information transmission and communication technologies to a new paradigm. It relies on quantum entanglement to facilitate the transmission of quantum states between parties. Quantum repeaters are crucial for facilitating long-distance quantum communication. These quantum devices act as intermediaries between adjacent communication channel segments within a fragmented quantum network, allowing for entanglement swapping between the channel segments. This entanglement swapping process establishes entanglement links between the endpoints of adjacent segments, gradually creating a continuous entanglement connection over the entire length of the transmission channel. The established quantum link can be utilized for secure and efficient quantum communication between distant sender and receiver nodes. This study focuses on quantum entanglement purification, a protocol aimed at maintaining high fidelity entangled states above the operational threshold of the communication channel. This study investigates the optimal stage for executing the purification protocol and applies optimization schemes to evaluate various purification protocols. We use IBM Qiskit for circuit implementation and simulation. The results offer valuable insights into future approaches to implementing practical quantum repeaters and shed light on existing and anticipated challenges.