Purification of the residual entanglement

Optimal routing and end-to-end entanglement distribution in quantum networks

Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.

Entanglement-Assisted Entanglement Purification

The efficient generation of high-fidelity entangled states is the key element for long-distance quantum communication, quantum computation, and other quantum technologies, and at the same time the most resource-consuming part in many schemes. We present a class of entanglement-assisted entanglement purification protocols that can generate high-fidelity entanglement from noisy, finite-size ensembles with improved yield and fidelity as compared to previous approaches. The scheme utilizes high-dimensional auxiliary entanglement to perform entangling nonlocal measurements and determine the number and positions of errors in an ensemble in a controlled and efficient way, without disturbing the entanglement of good pairs. Our protocols can deal with arbitrary errors, but are best suited for few errors, and work particularly well for decay noise. Our methods are applicable to moderately sized ensembles, as will be important for near term quantum devices.

Feasible measurement-based entanglement purification in linear optics

Entanglement purification is used to distill high quality entangled states from several noisy low quality entangled states, and it plays a key role in quantum repeater. The measurement-based entanglement purification protocol (MB-EPP) does not require local two-qubit gates or single-particle measurements on the noisy pairs and may offer significant advantages compared with the gate-based EPPs. We present an alternative MB-EPP in linear optics. Subsequently, we provide a detailed analysis on the realization of this MB-EPP using spontaneous parametric down conversion (SPDC) sources. By delicately designing the optical circuits, the double-pair emission noise caused by SPDC sources can be eliminated automatically. Combined with suitable quantum memory and entanglement swapping, this MB-EPP may have application potential in the implementation of a practical measurement-based quantum repeater.

Feasible time-bin entanglement purification based on sum-frequency generation

High quality time-bin entanglement is widely exploited to achieve the purposes of fundamental tests of physics and the implementation of quantum communication protocols both in free space and optical fiber propagation. However, the imperfect approaches of generating time-bin entangled state will degrade its quality and limit its practical application. Entanglement purification is to distill high quality entangled states from low quality entangled states. In this paper, we present the first entanglement purification protocol (EPP) for time-bin entanglement. We first explain this EPP for two-photon time-bin entangled state and then extend it to the system of multi-photon time-bin entangled state. We also design a possible realization of this EPP with practical spontaneous parametric down conversion (SPDC) source. Differ from the conventional EPPs, this EPP does not require the sophisticated controlled-not (CNOT) gate or similar operations, and it uses the feasible sum-frequency generation (SFG) to perform the purification. Moreover, the double-pair noise emitted from the SPDC source can be eliminated automatically which is the other advantage of this EPP. If we combine with the faithful entanglement swapping, this EPP may have potential to be a part of full quantum repeaters.

Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters

Solid quantum repeater is a core part in a large-scale quantum network. Entanglement purification, the key technique in a quantum repeater, is used to distill high-quality nonlocal entanglement from an ensemble in a mixed entangled state and to depress the vicious influence on quantum information carriers caused by noise. Here, we present an imperfect-interaction-free entanglement purification on nonlocal electron spins in quantum dots for solid quantum repeaters, using faithful parity check on electron spins. The faithful parity check can make correct judgement on the parity mode without destructing the nonlocal solid entanglement even with the imperfect interaction between a QD embedded inside a microcavity and a circularly polarized photon in the nearly realistic condition. Therefore, the imperfect-interaction-free entanglement purification can prevent the maximally entangled states from being changed into partially entangled ones and guarantee the fidelity of the nonlocal mixed state to a desired one after purification. As this scheme is feasible in the nearly realistic condition with imperfect interaction, the requirements for experimental implementation will be relaxed. These distinctive features make this imperfect-interaction-free entanglement purification have more practical applications in solid quantum repeaters for a large-scale quantum network.