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Journal of Physics A Mathematical and Theoretical

Single-photon entanglement purification procedure with path length fluctuations

Jin Woo Jun

Published Jan 10, 2013• 1 citation
Publisher

Abstract

According to the recent experiment of Salart et al (2010 Phys. Rev. Lett. 104 180504) on the single-photon entanglement purification procedure with path length fluctuations, the improvement of the degree of entanglement is as high as 4.5%. On the other hand, it has been shown in Sangouard et al (2008 Phys. Rev. A 78 050301) that the optimal theoretical value is 5.7%. We find that the remaining 1.2% may be due to the environmental effects of the phase flip noise or the amplitude noise and that it may not be due to the bit flip noise.

DOI
10.1088/1751-8113/46/4/045305

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According to the recent experiment of Salart et al (2010 Phys. Rev. Lett. 104 180504) on the single-photon entanglement purification procedure with path length fluctuations, the improvement of the degree of entanglement is as high as 4.5%. On the other hand, it has been shown in Sangouard et al (2008 Phys. Rev. A 78 050301) that the optimal theoretical value is 5.7%. We find that the remaining 1.2% may be due to the environmental effects of the phase flip noise or the amplitude noise and that it may not be due to the bit flip noise.
Recently Xiao et al. proposed a scheme for entanglement purification based on doubly entangled photon states (Phys. Rev. A 77(2008) 042315). We modify their scheme for improving the efficiency of entanglement purification. This modified scheme contains two steps, i.e., the bit-flip error correction and the entanglement purification of phase-flip errors. All the photon pairs in the first step can be kept as all the bit-flip errors are corrected. For purifying the phase-flip errors, a wavelength conversion process is needed. This scheme has the advantage of high efficiency and it requires the original fidelity of the entangled state wanted fay lower than other schemes, which makes it more feasible in a practical application.
Entanglement purification is a vital protocol to produce a high-quality entangled state from an ensemble of identical states. Based on the particular scheme of entanglement purification [Phys. Rev. A 87, 052316 (2013)], the effect of phase fluctuation is investigated. The convergence pattern of the initial states can be divided into two kinds of regions, corresponding to the purified outcomes being a maximally entangled state (MES) or a separable state. And there is the fractal-like structure near the boundary between these two regions. It is found that the phase noise plays a positive role in generating an MES for an initial states near some fractal boundary, which can only become the separable one if the noise is absent. It is also found that the minimal iteration steps to achieve the maximally entangled state with the phase noise can be decreased, which can save the resource in the protocol.
Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network.
Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.
High-dimensional quantum entanglement offers significant advantages over its two-dimensional counterparts in various quantum information processing tasks. We propose a scalable method for implementing an arbitrary high-dimensional entanglement purification protocol (HDEPP) using path superposition. By selecting appropriate single-qudit gates, qudit-flip errors and phase-flip errors can be purified. Counterintuitively, the HDEPP becomes more robust for higher-dimensional systems and exhibits enhanced purification fidelity as the dimension increases. Our HDEPP not only requires fewer operational resources but also in principle can achieve unity fidelity through multiple rounds of iteration. Furthermore, we develop feasible optical schemes to purify the frequency degree of freedom of photons suffering from qudit-flip and phase-flip errors using hyperentanglement. This work paves the way toward high-dimensional quantum communication and quantum networks.