Entanglement purification is a quantum network protocol used to improve the quality of entanglement and counteract the impact of noise. As entangled states are propagated across a quantum network, they accumulate noise, which reduces entanglement quality. Purification helps combat noise by producing a small number of high-quality pairs from a series of low-quality pairs.
When two end nodes request entanglement on a quantum network, a series of operations is kicked off. Each of these operations decreases the quality of the resulting pair. There are different methods for generating entanglement, but connections on near-term networks are always subject to the impact of noise. Entanglement purification offers a method of maintaining entanglement quality despite the presence of noise.
Entanglement purification consumes multiple low-quality entangled pairs to generate a smaller number of high-quality pairs. Quality of entangled pairs is typically measured by fidelity. Often, an application will require a specific fidelity in order to function properly. Purification can be used to ensure the network can provide the required fidelity. For example, suppose the network can generate pairs with a fidelity of .6. Using entanglement purification, it might be possible to convert four pairs with a fidelity of .6 into a single pair at a fidelity of .9, making it suitable for the application.
Entanglement purification has several important consequences that impact the development of quantum networks:
- Bootstrapping entanglement quality: Even near-term lossy networks can be “bootstrapped” to generate high-quality entanglement.
- Noise-rate tradeoff: Purification shifts the tradeoff from noise and quality to bandwidth.
- Timing and memories: Purification operations and their corresponding classical signals take time. Quantum state needs to last long enough to make this additional wait time worthwhile.
- Round-trip classical communication: A fundamental limit of entanglement purification is its reliance on round-trip classical communication. This fundamentally links bandwidth to distance.