Quantum

From Qubit Tensorization to Gaussian Optimizers in Bosonic Systems

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Briefings

A new method derives Gaussian optimality results for bosonic quantum systems by lifting qubit inequalities to large qubit systems using pseudo-Weyl operators. The research establishes that the sharp 2-logarithmic Sobolev inequality for bosonic Ornstein-Uhlenbeck semigroups tensorizes without loss in the constant, and provides a sharp output entropy inequality for tensor powers of qubit channels, including a quantum Mrs. Gerber's lemma for the depolarizing channel.

Key points

• The sharp 2-logarithmic Sobolev inequality for bosonic Ornstein-Uhlenbeck semigroups tensorizes without loss in the constant.
• A sharp output entropy inequality for tensor powers of qubit channels is established, including a quantum Mrs. Gerber's lemma for the depolarizing channel.

Context

This work extends Gross's derivation of the Gaussian logarithmic Sobolev inequality to bosonic systems by using qubits as quantum two-point spaces and lifting Weyl operators to pseudo-Weyl operators on large qubit systems.

Limitations

The evidence is a preprint from arXiv:2610.28902v1, with no peer review or experimental validation. Results are theoretical and limited to the fluctuation limit and specific channel classes.

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