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Laser Physics

Error-rejecting entanglement purification and concentration for one-dimensional waveguide-emitter system

Fang‐Fang Du, Linghui Li, Xue-Mei Ren, Yangyang Wang, Wenyao Liu

Published Oct 4, 2024• 1 citation
Publisher

Abstract

Abstract The distribution of maximal entanglement stands as a pivotal technique in long-distance practical quantum communication. Specifically, achieving high-fidelity entanglement distribution leans upon efficacious entanglement purification and entanglement concentration. In this paper, we materialize error-rejecting nonlocal entanglement purification protocol (EPP) and entanglement concentration protocol (ECP) for solid-state emitter systems assisted by the scattering property of photon-emitter in one-dimensional waveguide. The parity-check gates of both the EPP and ECP can herald the faulty events with the help of the detectors that click, so they are accomplished, in principle, with unity fidelities, which are conducive to implement two protocols. Moreover, additional emitters are unnecessary except a single photon.

DOI
10.1088/1555-6611/ad7c33

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Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocol, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve the efficiency of long-distance quantum communication exponentially. Meanwhile, it will be shown that this EPP can be used to complete nonlocal Bell-state analysis perfectly. We also discuss this EPP in a practical transmission.
The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication. Here we present a heralded two-photon entanglement purification protocol (EPP) using heralded high-fidelity parity-check gate (HH-PCG), which can increase the entanglement of nonlocal two-photon polarization mixed state. The HH-PCG is constructed by the input-output process of nitrogen-vacancy (NV) center in diamond embedded in a single-sided optical cavity, where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector. As the unwanted components can be filtrated due to the heralded function, the fidelity of the EPP scheme can be enhanced considerably, which will increase the fidelity of quantum communication processing.
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon with a certain probability, while the conventional ECPs require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second protocol is implemented with cross-Kerr-nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiments. With cross-Kerr-nonlinearities, it does not require sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it may be the most economical protocol by far. Meanwhile, both protocols are more suitable for multiphoton system concentration because they need less operations and classical communications. All these advantages make the two protocols useful in current long-distance quantum communications.
We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F > 1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.