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Journal of the Korean Physical Society

Single-photon entanglement purification procedure in a squeezed generalized amplitude damping channel

Jin Woo Jun

Published Sep 1, 2015• 0 citations
Publisher

Abstract

Analyzing the effects of the squeezed generalized amplitude damping noise on the single-photon entanglement purification procedure with path length fluctuations, we find that, for large value of T, the amplitude noise becomes as important as the phase flip noise in the role of origin of the discrepancy between the experimental value 0.796 of Salart et al . (Phys. Rev. Lett. 104 180504, 2010) and the theoretical value of 0.808 of Sangouard et al . (Phys. Rev. A 78 050301, 2008).

DOI
10.3938/jkps.67.771

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Analyzing the effects of the squeezed generalized amplitude damping noise on the single-photon entanglement purification procedure with path length fluctuations, we find that, for large value of T, the amplitude noise becomes as important as the phase flip noise in the role of origin of the discrepancy between the experimental value 0.796 of Salart et al . (Phys. Rev. Lett. 104 180504, 2010) and the theoretical value of 0.808 of Sangouard et al . (Phys. Rev. A 78 050301, 2008).
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.
A squeezed generalized amplitude damping (SGAD) channel is a quantum channel that models a general noise process incorporating the effects of bath squeezing, dissipation, and decoherence. In this paper, we analyze the dynamics of quantum entanglement and discord in the SGAD channel with memory. By obtaining a stochastic map defining this noisy quantum channel, we derive the concurrence and discord of Werner-like mixed states sent by successive uses of the channel. It is shown that these quantum correlations can be preserved or even generated depending on the initial channel input states, channel parameters, and the degree of channel memory. In particular, the squeezing effect does not contribute to the dynamics of quantum correlation for singlet-like states under correlated noise.
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.
Entanglement is an important resource for various applications of quantum computation. Another important endeavor is to establish the role of entanglement in practical implementation where system of interest is affected by various kinds of noisy channels. Here, a single classical bit is used to send information under the influence of a noisy quantum channel. The entanglement content of quantum states is computed under noisy channels such as amplitude damping, phase damping, squeesed generalised amplitude damping, Pauli channels and various collective noise models on the protocols of quantum key distribution.
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.
Abstract The inherent association between real quantum systems and their surrounding environment invariably results in decoherence, leading to the loss of entanglement. This diminution in entanglement coincides with a decline in the fidelity of transmitted information using the entangled quantum resource. This study scrutinizes the impact of the squeezed generalized amplitude damping (SGAD) channel on quantum Fisher information (QFI) parameters. The SGAD channel model, a versatile framework, is also employed to simulate other dissipative channels, including amplitude damping (AD) and generalized amplitude damping (GAD). Kraus operators facilitate the modeling of noisy channels. The results reveal that, within the SGAD channel, the QFI remains impervious to the squeezing variables (r and Φ\PhiΦ Φ ). In the GAD channel, FθGADF\theta _{GAD}FθGAD​ F θ GAD undergoes enhancement to a constant value with an upswing in temperature (T), while the ϕ\phiϕ ϕ parameter in the GAD channel, FϕGADF\phi _{GAD}FϕGAD​ F ϕ GAD , akin to the SGAD channel, surges around T = 2 before complete loss ensues. Concerning the AD channel, the θ\thetaθ θ component of the QFI initially experiences decoherence with an augmentation in the AD noise parameter ( λ\lambdaλ λ ). Subsequently, it is restored to its initial value with a further escalation in λ\lambdaλ λ . Conversely, the ϕ\phiϕ ϕ component of the QFI in the AD channel experiences decoherence with an elevation in the AD noise parameter ( λ\lambdaλ λ ).