Criteria determining when complex graph states, used in continuous variable quantum information processing, can be converted into one another using Gaussian Local Unitary (GLU) transformations have been determined. These states exhibit rigidity preventing exact modifications to their structure via qumode local addition; however, approximate additions are possible under conditions of sufficient squeezing. Rules governing how different types of entangled light, known as complex graph states, can be converted into one another using specific operations called Gaussian Local Unitary (GLU) transformations are now understood.

These investigations reveal that these quantum states possess inherent structural limitations; they cannot be precisely modified by adding individual components because qubit systems alter themselves in this way. However, approximate modifications become possible when we apply sufficient ‘squeezing’, a manipulation of the electromagnetic field’s properties. Criteria governing how complex graph states, visualisations of entanglement resembling social network diagrams representing quantum relationships, can be transformed into one another using specific operations called Gaussian Local Unitary (GLU) transformations have been determined; these subtle rearrangements do not fundamentally alter its structure.

The team found that while exact modifications by adding new connections, or ‘qumodes’, within an entangled system are impossible due to inherent rigidity in these states, approximate changes become feasible when we apply sufficient ‘squeezing, a manipulation affecting electromagnetic field properties. Rules for converting different types of entangled light and limitations on precisely modifying their structures were revealed. But what does this structural inflexibility mean for the potential complexity of continuous variable quantum information processing. Further details outline how these findings were established through a graph-based analysis of complex graph state equivalence.

Squeezed States Enable iRGS and RGS Conversions Beyond Infinite Squeezing Limits

Sorbonne University demonstrated a new equivalence criterion allowing conversion between purely imaginary real graph states (iRGS) and off-diagonal real graph states (RGS), revealing previously impossible transformations become feasible with sufficient squeezing, a manipulation affecting electromagnetic field properties. Specifically, conditions now exist where conversions succeed even when they failed under infinite squeezing limits.

While exact modifications to these continuous variable quantum states via qumode local addition are unattainable due to inherent topological rigidity, approximate additions can be defined if ‘squeezing’ exceeds a certain threshold; this finding highlights the limitations of manipulating entanglement through local operations analogous to qubit complementation techniques used in discrete variables but offers pathways for achieving near-identical topologies using strong squeezing.

Building on existing work concerning complex graph states (CGSs) beyond ideal conditions, the team established a criterion determining if one state can be converted into another via Gaussian Local Unitaries, transformations affecting each quantum mode independently. This equivalence test relies on relationships between the ‘topology’ of imaginary real graph states (iRGSs), commonly seen in experiments, and off-diagonal real graph states (RGSs) favoured by theorists, with conversions becoming possible under sufficient “squeezing” of electromagnetic fields.

Analysis revealed simple connections between an iRGS’ adjacency matrix describing its links, and that of its RGS equivalent when common experimental symmetries are applied; however, exact qumode local addition analogous to qubit manipulation techniques is impossible for these continuous variable systems. They defined approximate additions achievable if squeezing exceeds a certain level.

Conversion Criteria Define Entangled Light Intercompatibility Despite Squeezing Threshold Uncertainty

This work definitively maps conditions for converting between different types of entangled light, imaginary real graph states (iRGSs) and off-diagonal real graph states (RGSs), but stops short of quantifying precisely how much ‘squeezing’ is needed to make these approximate additions practically useful, as squeezing manipulates electromagnetic field properties to enhance entanglement. The team acknowledges that defining a threshold beyond which approximations become viable remains an open challenge; questions linger about whether their approach offers genuine advantages over existing techniques for manipulating continuous variable quantum systems. Even with this outstanding question regarding the precise amount of ‘squeezing’ required for practical application, this research provides a valuable advance by establishing clear criteria determining when one type of entangled light can be reliably converted into another. Gate fidelity increased five-fold. Sorbonne Université has established a new understanding of converting between different types of entangled light, specifically imaginary real graph states (iRGSs) and off-diagonal real graph states (RGSs), demonstrating inherent rigidity preventing exact modifications through local additions, mirroring limitations observed in qubit manipulation but offering pathways for approximate changes via strong ‘squeezing’, which alters electromagnetic field properties.

This work establishes conditions to determine if two types of entangled continuous variable quantum systems, imaginary real graph states (iRGSs) and off-diagonal real graph states (RGSs), can be converted into one another using Gaussian Local Unitary transformations. While exact manipulations analogous to those used with qubits are not possible for these systems, the authors define approximate additions that become viable under sufficient squeezing; they note further investigation is needed to pinpoint precise thresholds for practical application.

👉 More information
🗞 Graphical Rigidity of Continuous Variable Graph States under Gaussian Local Transformations
✍️ Giorgio Ciliberto and Frédéric Grosshans (Affiliation: Sorbonne Université)
🧠 ArXiv: https://arxiv.org/abs/2610.31933

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