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Optics Express

High-efficient entanglement distillation from photon loss and decoherence

Tie-Jun Wang, Chuan Xi Wang

Published Nov 24, 2015• 18 citations
Publisher

Abstract

We illustrate an entanglement distillation protocol (EDP) for a mixed photon-ensemble which composed of four kinds of entangled states and vacuum states. Exploiting the linear optics and local entanglement resource (four-qubit entangled GHZ state), we design the nondemolition parity-checking and qubit amplifying (PCQA) setup for photonic polarization degree of freedom which are the key device of our scheme. With the PCQA setup, a high-fidelity entangled photon-pair system can be achieved against the transmission losses and the decoherence in noisy channels. And in the available purification range for our EDP, the fidelity of this ensemble can be improved to the maximal value through iterated operations. Compared to the conventional entanglement purification schemes, our scheme largely reduces the initialization requirement of the distilled mixed quantum system, and overcomes the difficulties posed by inherent channel losses during photon transmission. All these advantages make this scheme more useful in the practical applications of long-distance quantum communication.

DOI
10.1364/oe.23.031550

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We illustrate an entanglement distillation protocol (EDP) for a mixed photon-ensemble which composed of four kinds of entangled states and vacuum states. Exploiting the linear optics and local entanglement resource (four-qubit entangled GHZ state), we design the nondemolition parity-checking and qubit amplifying (PCQA) setup for photonic polarization degree of freedom which are the key device of our scheme. With the PCQA setup, a high-fidelity entangled photon-pair system can be achieved against the transmission losses and the decoherence in noisy channels. And in the available purification range for our EDP, the fidelity of this ensemble can be improved to the maximal value through iterated operations. Compared to the conventional entanglement purification schemes, our scheme largely reduces the initialization requirement of the distilled mixed quantum system, and overcomes the difficulties posed by inherent channel losses during photon transmission. All these advantages make this scheme more useful in the practical applications of long-distance quantum communication.
As the interaction between the photons and the environment which will make the entangled photon pairs in less entangled states or even in mixed states, the security and the efficiency of quantum communication will decrease. We present an efficient hyperentanglement purification protocol that distills nonlocal high-fidelity hyper-entangled Bell states in both polarization and spatial-mode degrees of freedom from ensembles of two-photon system in mixed states using linear optics. Here, we consider the influence of the photon loss in the channel which generally is ignored in the conventional entanglement purification and hyperentanglement purification (HEP) schemes. Compared with previous HEP schemes, our HEP scheme decreases the requirement for nonlocal resources by employing high-dimensional mode-check measurement, and leads to a higher fidelity, especially in the range where the conventional HEP schemes become invalid but our scheme still can work.
High-dimensional hyperentangled states, serving as crucial physical resources in quantum communication, have attracted significant attention due to their exceptional properties (e.g., higher information density) compared to conventional two-dimensional single-degree-of-freedom entanglement. However, practical quantum entanglement systems inevitably suffer from environmental interactions, resulting in their degradation into partially entangled pure states or even mixed states, thereby significantly compromising the efficiency and security of quantum communication. Consequently, improving entanglement preservation in noisy systems emerges as a pivotal challenge in realizing fault-tolerant quantum networks. We propose two universal distillation schemes based on local positive-operator-valued measures (POVMs) for single-copy $(2\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4)$-dimensional hyperentangled photons. These schemes effectively suppress photon vacuum errors induced by transmission losses and are constructed using spatial-mode and polarization-based POVM measurements, respectively. Our results demonstrate that the spatial-mode-based scheme outperforms its polarization-based counterpart in terms of fidelity and success probability. Remarkably, we discover that with appropriate POVM parameters, the fidelity range of amplitude-damped noisy states can be expanded to cover almost all parameter spaces. Due to the universal applicability of POVM measurements, which require neither auxiliary entanglement nor complex detectors and operate on single copies of imperfect states in each purification round, our scheme provides an experimentally feasible solution for distilling high-dimensional hyperentangled photonic states.
Inherent channel losses during photon transmission limit the efficiency of optical quantum communication. In this paper, we construct a hyperdistillation scheme which can be used to distill the spatial-mode and polarization states of a photon simultaneously from photon loss in a heralded strategy. Exploiting linear-optical devices, the fidelity of a single-photon two qubit in a lossy signal mode can be increased to one with a certain success probability. By using a four-photon entanglement resource, the success probability of the hyperdistillation operation could be improved. The proposed scheme provides a realistic solution to overcome the transmission losses and exhibits unique properties, which shows important applications to quantum information processing.
We present a practical entanglement distillation protocol (EDP) with linear optics for a genuine mixed state. Each components of the genuine mixed state is a pure less-entangled state. After successfully performing this EDP, we can obtain a high quality entangled mixed state. Our EDP can work for both ideal entanglement sources and current available spontaneous parametric down-conversion (SPDC) sources, which makes it feasible in current experimental technology. Moreover, by using the SPDC source, we can obtain a higher fidelity. This protocol can also be used to distill the multi-partite entangled systems. All the features make it practical and useful in current quantum communications.
We investigate a new approach for achieving hyperdistillation and hyperentanglement purification operations simultaneously on two-photon systems, whose state is described by nonlocal hyperentangled Bell states on both the spatial mode and polarization degree of freedoms. Exploiting linear optics and local entanglement resource, the quantum nondemolition (QND) parity-checking measurement and the heralded two-qubit amplification could are key steps in our scheme. With the QND parity-checking measurement and heralded qubit amplification operations, both the bit-flip (phase-flip) errors caused by decoherence in noisy channels and the vacuum errors caused by the transmission losses can be corrected. We show that the proposed scheme provides a new solution to overcome the problem of photon losses and decoherence simultaneously, which could be achieved with current technologies.
The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some high-quality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.