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Researchers have proven that including at least one Gaussian state in an ensemble guarantees a unique, well-defined average quantum state within the framework of Quantum Optimal Transport. This result establishes the mathematical rigidity required for reliable computation of barycenters, bridging the gap between complex quantum distributions and their classical counterparts. The findings provide a critical theoretical foundation for stabilizing quantum transport calculations without requiring all input states to be perfectly Gaussian.

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Researchers Find Gaussian States Yield Unique Quantum Transport Barycentres

Quantum ZeitgeistOctober 4, 20264 min read

Until now, determining whether combinations of quantum states would themselves remain predictably Gaussian has remained an open problem. This work demonstrates that providing even one ‘faithful’ Gaussian input guarantees both a uniquely defined and entirely Gaussian resulting barycenter, a result previously unproven. Furthermore, it establishes how these quantum solutions converge towards their classical counterparts in transport theory.

Can reliably compute uniquely defined average quantum states exist from an ensemble of inputs. A framework for Quantum Optimal Transport barycenters, the quantum analogue of classical Wasserstein barycenters, now exists alongside proofs showing that if even one input state is suitably well-behaved, then the resulting averaged state will also be both unique and necessarily Gaussian. Principles governing Quantum Optimal Transport barycenters have been established; these calculations average multiple quantum states into one. Having at least one well-behaved initial state,…

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