Researchers Bound Cryptographic Leakage in GKP State Aggregation

Nilesh Vyas, Airbus Central R&T, and colleagues have created an active, measurement-based framework for aggregating multiple Gottesman-Kitaev-Preskill (GKP) states, overcoming limitations of passive linear optics that compressed the phase-space lattice and caused quantum data loss. The method preserves the code space geometry up to correctable deformations, achieving a lattice spacing of √π, an improvement on the √2π resulting from previous passive approaches. A new technique combines quantum information across a network, resolving a key limitation in continuous-variable quantum computing systems.

The team addressed issues stemming from signal loss and distortion when employing conventional optical methods, enabling more dependable and geometrically-precise aggregation of quantum states. This provides a theoretical basis for constructing secure and strong quantum networks utilising this approach, allowing for the preservation of the structure of quantum data during aggregation. The researchers R&T developed a new method for combining quantum information across a network, addressing a key obstacle in continuous-variable quantum computing.

They tackled the problem of signal loss and distortion that occurs when using traditional optical techniques to merge quantum states, enabling more reliable and geometrically-accurate aggregation. This is achieved using Gottesman-Kitaev-Preskill (GKP) coding, which encodes quantum information using the position and momentum of light, similar to how a vinyl record stores information in its grooves. The new framework preserves the structure of quantum data during aggregation, allowing for the construction of secure and strong quantum networks, though scaling this approach requires careful consideration of error accumulation during merging.

Optimised quantum aggregation via active error correction and GKP states

Airbus Central R&T personnel achieved a lattice spacing of √π in aggregated quantum states, a substantial improvement over the √2π previously attainable with passive linear optics. The team’s active, measurement-based framework utilises GKP Bell states and homodyne feed-forward to compute the logical sum of distributed states while preserving code space geometry; active correction of errors is a key departure from prior passive methods.

Analytical fidelity limits demonstrate that achieving over 99% operational fidelity requires approximately 13.8 decibels of optical squeezing for a two-node network, increasing to 22.1 decibels for sixteen nodes, showing scalability. Monte Carlo simulations, utilising 30,000 trials per configuration, revealed that accumulated network noise scales proportionally to the square root of the number of nodes, meaning larger networks necessitate greater initial squeezing to maintain precision. The protocol operates as an approximate quantum non-demolition measurement, enabling syndrome extraction without collapsing the quantum state.

However, even with high squeezing levels, practical photon loss in optical fibres introduces an irreducible vacuum noise floor, currently limiting the maximum achievable fidelity and demonstrating a clear gap remains before deployment in real-world conditions. Experiments were conducted across network sizes of 2, 4, 8, and 16 nodes to assess noise accumulation during the aggregation of quantum states, ensuring reliable statistical results.

Active Error Correction via Homodyne Feed-Forward for Symplectic Lattice Compression

Homodyne feed-forward, a technique akin to noise cancellation in headphones, was employed by the team to actively correct errors as they arose during the aggregation process. This method addresses symplectic lattice compression, a stretching of the space where quantum information is encoded, making accurate readings difficult, by actively reshaping the quantum data. A continuous-variable quantum key distribution protocol employing GKP codes, a method for encoding quantum information in the phase of light, was evaluated to enable distributed quantum computing.

Optical squeezing varying from 5.0 to 30.0 decibels was used to reduce noise and improve signal clarity; this squeezing determined the initial variance of single quantum modes. This approach allows for more precise and reliable quantum computations across a network by preserving the geometry of the encoded information.

Active error correction combats decoherence in quantum networks

Reliably sharing delicate quantum states across a network is the promise of distributed quantum computing, yet maintaining their integrity proves exceptionally challenging. An active framework, correcting errors as they emerge, offers a compelling alternative to simply amplifying signals, a strategy increasingly ineffective as network complexity grows. The team acknowledges that even minor photon loss within fibre optic cables creates an unavoidable noise floor, introducing a vulnerability inherent in precise, continuous measurement.

This active framework represents a departure from passive methods, which struggle with the compression of the phase space lattice and subsequent loss of data. By employing GKP Bell states and this noise-cancellation technique, the personnel constructed a system that computes the combined state of multiple quantum nodes while maintaining the geometry of the encoded information.

The researchers demonstrated a method for combining quantum information distributed across multiple nodes, utilising GKP codes and active error correction. This approach addresses challenges arising from signal compression and data loss inherent in transmitting quantum states, preserving the geometry of the encoded information. Analytical limits on logical fidelity were derived under constraints of optical squeezing, ranging from 5.0 to 30.0 decibels, and the team suggests further work could focus on bounding cryptographic leakage for continuous one-time pads.