Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

Abstract

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.

On the spectral nature of entanglement

“…These gates inherently generate a series of errors, specifically, three types: bit flip (X-errors), phase flip (Z-errors, or phase damping), and bit-phase flip [45]. The aforementioned link will also allow a better understanding of aspects related to decoherence [14,15] in non-adiabatic environments, as well as a very common process present in all real quantum channels known as the amplitude damping [46].…”

Optimizing practical entanglement distillation

“…We note that it has been recently shown that the DE-JMPS protocol achieves the highest possible fidelity over LOCC operations when distilling a two-qubit state from two copies of a Bell diagonal state of rank two [42]. Moreover, in [41] protocols that permute Bell states in the mixture were analyzed and it was claimed that for two copies of all Bell diagonal states, DEJMPS protocol achieves the highest achievable fidelity when distilling a two-qubit state, but only among all such permuting protocols.…”

Guest Editorial Advances in Quantum Communications, Computing, Cryptography, and Sensing

“…Furthermore, sophisticated quantum repeater protocols need to be developed for mitigating the errors introduced by the channels, which may be partly addressed through quantum error correction codes. In the absence of coding, the losses may be dealt with by heralded entanglement generation, while the error probability may be reduced by entanglement distillation (see e.g., [29]). Despite all these potential approaches, practical realization of quantum repeaters remains an open technical challenge.…”