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Acta Physica Sinica

Quantum entanglement concentration for photonic polarization state assisted by electron spin

Zhao Rui-Tong, Ruisheng Liang, Wang Fa-Qiang

Published Jan 1, 2017• 2 citations
Publisher

Abstract

In order to assure the security of the long-distance quantum communication, the maximum entangled state is necessary. However, the decoherence of the entanglement is inevitable because of the channel noise and the interference of the environment. Quantum entanglement concentration can be used to convert a non-maximum entangled state into a maximum one. In previous entanglement concentration proposals, we need the initial coefficients of non-maximum entangled state or repeat the entanglement concentration process to improve the possibility of success, which reduces the efficiency of the entanglement concentration. A more efficient entanglement concentration for phontonic polarization state is proposed in this paper, which is based on the interaction between circularly polarized light and quantum dot-cavity system. An auxiliary photon is introduced to connect two distant participants. To overcome the channel noise, the auxiliary photon transmits though two channels between the two participants. The photons interact with coupled quantum dot-cavity before and after the auxiliary photon transmission. Then the states of spins and auxiliary photon are measured, and the maximum phontonic polarization entangled state is obtained by single-photon operations according to the measurement results. The success possibility of the proposed scheme is 1 in ideal conditions, that is, the concentration can be realized deterministically. However, the cavity leakage is unavoidable, so the fidelity of the entanglement concentration is calculated by taking one of the measurement results for example. The results show that the influences of the initial coefficients of non-maximum entangled state on the fidelity can be ignored in most cases, which saves a mass of photons used to measure the initial coefficients of the non-maximum entangled state. The fidelities with varying coupling strengths and cavity leakages are also shown in the paper. In the case of weak coupling, the fidelity is low and varies sharply with cavity leakage. Fortunately, the fidelity will plateau in a strong coupling case, and reaches 99.8% with a coupling strength 0.7 for diverse cavity leakages. Much progress has been made in the study of the strong coupling between quantum dot and optical cavity, which can satisfy the requirement of our entanglement concentration. So the proposed scheme is feasible in the current experimental conditions. In general, our proposal still maintains high fidelity even considering the cavity leakage, and the initial information about partially entangled state and the repetition of the entanglement concentration process are not required. This not only improves the security of the quantum entanglement concentration, but also contributes to efficient quantum information processing with less quantum resources. These characteristics increase the universality and efficiency of the entanglement concentration, thus assuring the quality of the long-distance quantum entanglement.

DOI
10.7498/aps.66.240301

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In order to assure the security of the long-distance quantum communication, the maximum entangled state is necessary. However, the decoherence of the entanglement is inevitable because of the channel noise and the interference of the environment. Quantum entanglement concentration can be used to convert a non-maximum entangled state into a maximum one. In previous entanglement concentration proposals, we need the initial coefficients of non-maximum entangled state or repeat the entanglement concentration process to improve the possibility of success, which reduces the efficiency of the entanglement concentration. A more efficient entanglement concentration for phontonic polarization state is proposed in this paper, which is based on the interaction between circularly polarized light and quantum dot-cavity system. An auxiliary photon is introduced to connect two distant participants. To overcome the channel noise, the auxiliary photon transmits though two channels between the two participants. The photons interact with coupled quantum dot-cavity before and after the auxiliary photon transmission. Then the states of spins and auxiliary photon are measured, and the maximum phontonic polarization entangled state is obtained by single-photon operations according to the measurement results. The success possibility of the proposed scheme is 1 in ideal conditions, that is, the concentration can be realized deterministically. However, the cavity leakage is unavoidable, so the fidelity of the entanglement concentration is calculated by taking one of the measurement results for example. The results show that the influences of the initial coefficients of non-maximum entangled state on the fidelity can be ignored in most cases, which saves a mass of photons used to measure the initial coefficients of the non-maximum entangled state. The fidelities with varying coupling strengths and cavity leakages are also shown in the paper. In the case of weak coupling, the fidelity is low and varies sharply with cavity leakage. Fortunately, the fidelity will plateau in a strong coupling case, and reaches 99.8% with a coupling strength 0.7 for diverse cavity leakages. Much progress has been made in the study of the strong coupling between quantum dot and optical cavity, which can satisfy the requirement of our entanglement concentration. So the proposed scheme is feasible in the current experimental conditions. In general, our proposal still maintains high fidelity even considering the cavity leakage, and the initial information about partially entangled state and the repetition of the entanglement concentration process are not required. This not only improves the security of the quantum entanglement concentration, but also contributes to efficient quantum information processing with less quantum resources. These characteristics increase the universality and efficiency of the entanglement concentration, thus assuring the quality of the long-distance quantum entanglement.
Abstract We present error-rejecting entanglement concentration protocols (ECPs) for partially entangled electron spins in quantum dots (QDs) with unknown and known parameters using quantum electrodynamics of QDs coupled with optical cavities, which can recover the partially entangled state to the maximally entangled state with unit fidelity even in the non-ideal experimental condition. The error-rejecting ECP for a partially entangled state utilizes parity check operations on electron spins within QDs. Furthermore, for a partially entangled state with known parameters, the ECP is devised through a parameter-splitting approach. The success probabilities of these two error-rejecting ECPs can be further improved by using the resource recycling method and iteration method. On account of their unit fidelity and considerable success probability, the error-rejecting ECPs have promising application value in improving the fidelity of quantum communication.
A recent paper [Chuan Wang, Phys. Rev. A \textbf{86}, 012323 (2012)] discussed an entanglement concentration protocol (ECP) for partially entangled electrons using a quantum dot and microcavity coupled system. In his paper, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon. In this paper, we will present an optimal ECP for such entangled electrons with the help of only one single photon. Compared with the protocol of Wang, the most significant advantage is that during the whole ECP, the single photon only needs to pass through one microcavity which will increase the total success probability if the cavity is imperfect. The whole protocol can be repeated to get a higher success probability. With the feasible technology, this protocol may be useful in current long-distance quantum communications.
We present an efficient entanglement concentration protocol (ECP) for electron spins based on quantum-dot and microcavity coupled systems. In our ECP, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon, not two copies of two-electron spin systems. With current and near-future technology, the locally maximal entanglement of electron spins can be achieved, and our ECP can be used in long-distance quantum communications.
We demonstrate two entanglement concentration protocols (ECPs) for photon pairs in less-hyperentanglement, the simultaneous entanglement in multiple degrees of freedom. Using these ECPs, some maximally entangled states in polarization can be reconstructed deterministically from less-hyperentangled ones shared between remote participants. Both of the success probabilities are 100% in principle, and they do not require additional single photons. The former is implemented with the passive linear optics, which is achievable with current technology. The later adopts the cross-Kerr nonlinearity media to complete this task, which can increase the efficiency of the entanglement concentration process since it does not require the sophisticated single-photon detectors for measurements. The two ECPs are useful for practical long-distance quantum communication due to the fact that the entangled state in either the spatial degree of freedom or the frequency degree of freedom suffers little from channel noise in optical fiber.
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.
In recent years, quantum communication technology has developed rapidly, and quantum communication schemes based on hyperentangled states have attracted widespread attention due to their efficiency and security. However, in practical communication, maximally hyperentangled states are highly susceptible to environmental noise, which causes them to degrade into non-maximally hyperentangled states. This degradation significantly reduces the fidelity of the quantum information and communication efficiency. In this article, we propose an efficient entanglement concentration scheme to restore degraded polarization-time hyperentangled W states, thereby enhancing the reliability and transmission distance of multiparty quantum communication. The protocol employs the parameter-splitting approach, where the receiver performs local operations on received non-maximally hyperentangled photons by using linear optical elements, achieving hyperentanglement concentration through detector responses and post-selection. This method eliminates the need for auxiliary photons, thereby reducing the use of quantum resources and maintaining operational simplicity. Moreover, the scheme can be extended to N-photon hyperentangled W states. The theoretical calculations demonstrate that the success probability of the protocol is determined by the minimal parameter of the hyperentangled state, exhibiting a monotonic increase as this parameter grows. Under ideal conditions, the maximum success probability approaches unity and the success probability improves with the number of entangled photons increasing. When considering the efficiency of practical optical components, the maximal success probabilities for hyperentangled W states with N = 3, 4, and 5 are found to be 0.856, 0.791, and 0.732, respectively. Consequently, the proposed scheme efficiently concentrates the degraded polarization-time hyperentangled W state into the maximally hyperentangled state. This work is of significant importance for long-distance information transmission and provides theoretical references for implementing long-distance multi-party quantum communication.