Unravelling quantum internet’s secret weapon: How entanglement percolation connects the Quantum Future

But there’s a problem: entanglement is incredibly fragile. Sending it directly over long distances is like trying to carry water in a sieve. To overcome this intrinsic fragility, quantum networks rely on a clever strategy: first generating entanglement between neighboring nodes, and then propagating it across the network using quantum repeaters and memories. The challenge then becomes how to stitch these local entangled links together to create a strong, reliable connection between any two distant users.

This is where entanglement percolation comes in. Even if the initial connections in a quantum network are only non-maximally entangled (weak connections), entanglement percolation allows us to establish powerful, maximal entanglement between distant nodes under specific conditions. It’s the phenomenon that allows long-range quantum correlations essential for future quantum communication.

To achieve this, two crucial operations are employed:

• Entanglement swapping: imagine two separate entangled pairs (A-B and B-C) arranged in series. By performing a special measurement on the middle qubits (at node B) and sharing classical information, these two pairs can be combined into a single entangled pair (A-C). However, if the original states aren’t perfectly entangled, swapping actually amplifies initial imperfections, potentially yielding less entanglement in the final state than what you started with.
• Entanglement distillation: now, imagine two entangled pairs (A-B and A-B) arranged in parallel. Using local measurements and classical communication, you can take these two imperfect pairs and “distill” them into a single, more entangled state. Unlike swapping, distillation can improve the entanglement of its parent states and can even produce maximally entangled states from non-maximal ones, provided the initial imperfection isn’t too severe.

The art of connecting distant nodes lies in combining these two operations into a “quantum percolation strategy”.

A challenge in this field is finding the optimal sequence of swapping and distillation operations to connect distant users in complex networks, especially when the initial entanglement is noisy. This is precisely where the recent publication by QSNP partners from Polytechnic University of Bari, in collaboration with the University of Bari, makes a significant stride. The researchers developed a physics-informed heuristic algorithm to simulate and find optimal percolation paths in qubit-based planar quantum networks. This algorithm combines “locally optimal percolation strategies” and explores alternative paths to maximize the final entanglement while minimizing the number of “destroyed” (temporarily disconnected) states.

Through this analytical and numerical study, the researchers uncovered some key insights:

• Percolation thresholds: the study analytically determined and numerically verified “percolation thresholds”. These thresholds represent the minimum amount of entanglement the network’s initial states must possess for a given percolation strategy to successfully generate a maximally entangled state. They act as boundaries, defining distinct “connection phases” where optimal percolation is possible. Beyond these thresholds, networks enter an “entanglement decay” phase where achieving maximal entanglement becomes impossible.
• Network integrity (I(A,B)): to understand the real-world implications of these operations, the study introduced a new metric: network integrity. This quantifies how much of the network remains intact after a percolation process by measuring the ratio of the distance between connected nodes to the number of original entangled states destroyed during the process. If integrity drops below one, it means more states are being destroyed than theoretically necessary for the connection.
• Connectivity (K(A,B)): perhaps one of the most important contributions is the definition of “connectivity”. The researchers realized that simply maximizing end-user entanglement wasn’t enough, they needed a scale-free quantity that also accounted for the disruption to the network. Connectivity combines the entanglement of the final state with the network’s integrity, providing an indicator of the quality of the percolation process. On a regular lattice, this “connectivity” was found to be largely independent of the distance between users, primarily depending on the network’s topology and the quality of its initial nearest-neighbor entanglement.

The algorithm’s ability to detect these thresholds, even for complex “non-local” percolation strategies, is a testament to its effectiveness. The publication also explored how randomness in initial entanglement (quenched disorder) affects these processes, finding that while entanglement decay points remain consistent, a higher disorder can sometimes improve network integrity by unlocking more optimal paths.

This work represents a step forward in our understanding of quantum networks. By providing a powerful numerical tool and analytical framework, it helps us assess different network topologies and the inherent trade-offs between achieving long-distance entanglement and maintaining network integrity. The journey to the global Quantum Internet is long, but studies like this are crucial pieces of the puzzle, bringing us closer to a future where quantum communication reshapes our world.

Source

Percolation thresholds and connectivity in quantum networks

Andrea De Girolamo, Giuseppe Magnifico and Cosmo Lupo.

Quantum Science and Technology, Volume 10, Number 3