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Annalen der Physik

General Quantum Entanglement Purification Protocol using a Controlled‐Phase‐Flip Gate

Lu‐Cong Lu, Bao‐Cang Ren, Xin Wang, Mei Zhang, Fu‐Guo Deng

Published Mar 16, 2020• 9 citations
Publisher

Abstract

Abstract Entanglement purification is an important method to guarantee the fidelity of long‐distance quantum communication. Here, a general entanglement purification protocol (EPP) for mixed state with bit‐flip error and phase‐flip error is proposed, resorting to unilateral operations and a controlled‐phase‐flip (CPF) gate. The CPF gate is working with a high fidelity under balance condition of quantum dot embedded in a double‐sided optical cavity. This general EPP scheme can purify the mixed state with both bit‐flip error and phase‐flip error to a high fidelity entangled state relatively fast in some regimes, owing to the unilateral operations and high‐fidelity CPF gate, which can largely decrease the resource consumption. This general EPP provides a convenient way for increasing the entanglement of different quantum systems, which has great potential for guaranteeing the fidelity of long‐distance quantum communication in the future.

DOI
10.1002/andp.202000011

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Abstract Entanglement purification is an important method to guarantee the fidelity of long‐distance quantum communication. Here, a general entanglement purification protocol (EPP) for mixed state with bit‐flip error and phase‐flip error is proposed, resorting to unilateral operations and a controlled‐phase‐flip (CPF) gate. The CPF gate is working with a high fidelity under balance condition of quantum dot embedded in a double‐sided optical cavity. This general EPP scheme can purify the mixed state with both bit‐flip error and phase‐flip error to a high fidelity entangled state relatively fast in some regimes, owing to the unilateral operations and high‐fidelity CPF gate, which can largely decrease the resource consumption. This general EPP provides a convenient way for increasing the entanglement of different quantum systems, which has great potential for guaranteeing the fidelity of long‐distance quantum communication in the future.
Logic-qubit entanglement is a promising resource in quantum information processing, especially in future large-scale quantum networks. In the paper, we put forward an efficient entanglement purification protocol (EPP) for nonlocal mixed logic entangled states with the bit-flip error in the logic qubits of the logic Bell state, resorting to the photon-atom interaction in low-quality (Q) cavity and atomic state measurement. Different from existing EPPs, this protocol can also purify the logic phase-flip error, and the bit-flip error and the phase-flip error in physic qubit. During the protocol, we only require to measure the atom states, and it is useful for improving the entanglement of photon systems in future large-scale quantum networks.
Abstract We use the quantum-dots (QD) coupled with single-sided microcavities system to construct the error-rejecting controlled not (CNOT) gate of electronic spins system in QD; We have designed an error-rejecting entanglement purification protocol (EPP) of electronic spins system in QD by using the error-rejecting CNOT gate and unitary operation. It can extract the high entanglement from the mixed entanglement states of the electronic spins with low entangled states. This EPP can eliminate the operation errors caused by the nonideal interaction between photons and QD coupled with optical microcavities system, and improve the fidelity of the EPP through iteration. Our scheme is more practical in future long-distance quantum communications, especially providing significant benefits for solving decoherence problems in quantum networks and quantum repeaters.
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.
We present an entanglement purification protocol (EPP) to reconstruct some maximally hybrid entangled states (HESs) from nonmaximally mixed HESs. We use simple linear optical elements such as a polarization beam splitter (PBS) and beam splitter (BS) to achieve this task. Meanwhile, it is shown that the parity-check gates acted by PBS and BS are enough to complete the task, and the controlled-not (cnot) gates or similar logic operations are not needed. Unlike the current EPPs, this protocol can purify not only the conventional bit-flip error and phase-flip error but also the dissipation error coming from the photon loss of the coherent state. It can also be extended to achieve the purification for multiphoton and multicoherent state HES. This protocol may be useful in current hybrid quantum repeaters.
Entanglement purification is an indispensable ingredient in extended quantum communication networks and usually determines the efficiency and communication rate of quantum communication protocols. Different from all existing entanglement purification protocols (EPPs) where two or more copies of low quality mixed entangled states are selected from the same ensemble, here we describe a general and optimal EPP for arbitrary initial mixed states from different ensembles. We show that the successful operation of EPP may not obtain a higher fidelity mixed state, while the discarded source pair, which is usually regarded as a failure in existing EPPs, may have residual entanglement and can be reused to increase the yield of entanglement purification. We give the criterions of both the successful purification to obtain a higher fidelity mixed state and the existence of residual entanglement. Moreover, we reveal that entanglement purification procedure causes some entanglement loss. Finally, we provide an optimal approach to reduce the entanglement loss. This approach can also be used to increase the yield of entanglement purification. Our EPP may have potential application in long-distance quantum communications.
It has been found that logic-qubit entanglement has great potential for applications in quantum communication and quantum networks in recent years. However, along with the effects of noise and decoherence, the fidelity of the communication transmission can be greatly reduced. In this paper, we investigate the entanglement purification of logic bit-flip error and phase-flip error in polarization logic-qubit entanglement based on the parity-check measurement (PCM) gate, which is constructed by the cross-Kerr nonlinearity and used to distinguish the parity information of two-photon polarization states. The probability of entanglement purification is higher than the scheme using the linear optical method. Moreover, the quality of logic-qubit entangled states can be improved by a cyclic purification process. This entanglement purification protocol will be useful in the future when faced with long-distance communication with logic-qubit entanglement states.