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Efficient Recurrence Quantum Entanglement Distillation for PMD Channels

Liangzhong Ruan, Brian T. Kirby, Michael Brodsky, Moe Z. Win

Published Jun 22, 2017• 0 citations
OpenAlex

Abstract

Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing entanglement with high-quality via fiber optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences in the system. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements on both the size of the quantum circuits involved and on the initial quality of entanglement in particles. However, because the number of particles required grows exponentially with the number of rounds of distillation, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditional on the optimal fidelity being achieved) in every round of distillation. The attainment of optimal fidelity improves the convergence speed of fidelity with respect to the rounds of distillation from linear to quadratic, and hence significantly reduces the number of distillation rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with high fidelity via optic fibers.

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Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing entanglement with high-quality via fiber optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences in the system. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements on both the size of the quantum circuits involved and on the initial quality of entanglement in particles. However, because the number of particles required grows exponentially with the number of rounds of distillation, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditional on the optimal fidelity being achieved) in every round of distillation. The attainment of optimal fidelity improves the convergence speed of fidelity with respect to the rounds of distillation from linear to quadratic, and hence significantly reduces the number of distillation rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with high fidelity via optic fibers.
Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing high-quality entanglement via fiber-optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements both on the size of the quantum circuits involved and on the initial quality of entanglement between particles. However, because the number of required particles grows exponentially with the number of distillation rounds, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditioned on the fact that optimal fidelity is achieved) in every round of distillation. The attainment of the maximal fidelity improves the convergence speed of fidelity with respect to the number of distillation rounds from linear to quadratic and, hence, significantly reduces the number of rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with a high fidelity via optical fibers.
Quantum entanglement serves as a valuable resource for many important quantum operations. To address challenge brought by the noise in the quantum channel, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. To enable efficient QED algorithms, it is essential to increase the fidelity of the qubit pairs obtained in each rounds of distillation, so as to reduce the rounds of distillation required. This paper considers two-Kraus-operator (TKO) channels, a class that covers several typical quantum channels, characterizes the optimal fidelity achievable by QED operations in each round, and designs recurrence algorithms which achieve the optimal fidelity.
Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of implementability and robustness. However, the efficiency of recurrence QED algorithms has not been investigated thoroughly in the literature. This paper puts forth two recurrence QED algorithms that adapt to the quantum channel to tackle the efficiency issue. The proposed algorithms have guaranteed convergence for quantum channels with two Kraus operators, which include phase-damping and amplitude-damping channels. Analytical results show that the convergence speed of these algorithms is improved from linear to quadratic and one of the algorithms achieves the optimal speed. Numerical results confirm that the proposed algorithms significantly improve the efficiency of QED.
Quantum entanglement among remote agents is a key enabler for many important quantum communication operations. To establish entanglement between two remote agents, one agent can locally generate entangled qubit pairs and transmit one of the qubits in each pair to the other agent through quantum channels. However, the transmitted qubits will inevitably be contaminated by the noise inherent in the quantum channels. To address this challenge, quantum entanglement distillation (QED) algorithms have been developed to generate highly-entangled qubit pairs from many contaminated ones. Nevertheless, existing algorithms either have low efficiency or require large-scale quantum circuits. This paper focuses on phase-damping channel and proposes an efficient QED algorithm that only require small- scale quantum circuit.
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.
Future quantum networks offer the potential for new communication and computation applications. These quantum networks will undoubtedly require the routing of quantum information between distant parties. In order to reliably achieve the transmission of entangled states over such a network, some entanglement distillation protocol can be implemented on an ensemble of entangled photon pairs. Here, we demonstrate such a protocol by recovering quantum information using local filters on each photon of a polarization-entangled state in the presence of a common source of decoherence in the telecom fiber infrastructure, polarization mode dispersion (PMD).