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International Journal of Quantum Information

Polarization entanglement distillation through local filtering operations

Quan-Hai Sun, Guo‐Zhu Pan

Published Jun 1, 2018• 0 citations
Publisher

Abstract

An entanglement distillation scheme is proposed for an amplitude-damped polarization-entangled photon states via local filtering operations. The local filtering operations, i.e. positive operator-valued measure, on photons are realized by a series of Brewster window pairs. The entanglement of the survived photon pairs in the scheme will be much larger than that of the initial ones. In this sense, this distillation scheme is better than the currently existing entanglement protection scheme, where only the entanglement decaying time is prolonged and the entanglement is not enhanced at all. In addition, this scheme is simple and feasible within the current linear optical techniques.

DOI
10.1142/s0219749918500351

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An entanglement distillation scheme is proposed for an amplitude-damped polarization-entangled photon states via local filtering operations. The local filtering operations, i.e. positive operator-valued measure, on photons are realized by a series of Brewster window pairs. The entanglement of the survived photon pairs in the scheme will be much larger than that of the initial ones. In this sense, this distillation scheme is better than the currently existing entanglement protection scheme, where only the entanglement decaying time is prolonged and the entanglement is not enhanced at all. In addition, this scheme is simple and feasible within the current linear optical techniques.
In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach 1.01.01.0 for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.
We propose a scheme to enhance entanglement from amplitude damping or correlated amplitude damping decoherence. We show that entanglement sudden death time can be prolonged by the initial single-qubit operation combined with local filtering operation. For the amplitude damping channel case, we give the optimal single-qubit operation for arbitrary pure state [Formula: see text]. For the correlated amplitude damping channel case, we find that single-qubit operation on the initial state can not only enhance the final entanglement but also avoid entanglement sudden death. Compared to the previous schemes, the optimal operations and local filtering operations used in our scheme are independent with the decay parameters of the environment.
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.
Remote entanglement will inevitably decrease due to the interactions between quantum systems and their environments. Therefore protecting remote entanglement against decoherence is of great importance in realizing quantum communication and quantum comp utation. In this paper, we demonstrate that decoherence caused by weak-measurement-induced damping can be effectively suppressed by adding local unitary operation series on each qubit. The results show that the entanglement of the output state can approach that of the state before amplitude damping. The most distinct advantage of this entanglement protection scheme is that any unitary operation (except the identity operation) has this entanglement reversal effect on the amplitude-damped states. Furthermore, in each local unitary operation series, all the operations can be different from one other, and all the time intervals between any two adjacent operations can be different too. In addition, there is no need for the two remote users to synchronize their operations. Unlike most of the previous schemes, we do not assume the instantaneous local unitary operation, and each operation has a duration. All these advantages suggest that this remote entanglement protection scheme is much simpler and feasible than the previous ones, and we hope it can be implemented in the near future. Recently, Y. S. Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that ``pre-weak measurement +++ amplitude damping +++ bit-flipping operation +++ post-weak measurement'' can actively combat specific decoherence. By combing our proposal with Kim et al.'s scheme, the protection performance can be greatly improved by replacing the bit-flipping operation with an arbitrary rotational operation around the xxx axis, the number of the operations as well as the interval between any two adjacent operations all can be different, and the application range of the scheme can be greatly broadened.
Entanglement distillation has many applications in quantum information processing and is an important tool for improving the quality and efficiency of quantum communication, cryptography, computing, and simulation. We propose an entanglement distillation scheme using only one pair of polarization-frequency hyperentangled photons, which can be equivalently viewed as containing two pairs of entangled logical qubits: a pair of polarization-entangled qubits and a pair of frequency-entangled qubits. To perform the required CNOT operation between the two qubits we consider the use of a polarization-dependent frequency converter. Compared to past methods of entanglement distillation that relied on polarization and spatial-mode/energy-time degree of freedom, the utilization of frequency-encoded qubits offers an advantage in that it is immune to bit-flip errors when the channel is linear. After distillation, the fidelity of polarization entanglement can be significantly improved by sacrificing the frequency degree of freedom. Through simulation, we show that high fidelity gains, large yield, and high distillation rate can be achieved. Our distillation scheme is simple to implement with current technologies, compatible with existing telecommunication fiber networks, and is a promising approach for achieving efficient quantum communication.