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Quantum Tomography's Transition Has Two Shapes
New bounds close the near-boundary gap: diamond-norm tomography loses Heisenberg scaling immediately, while Choi trace norm changes gradually.
Summary
New bounds close the near-boundary gap: diamond-norm tomography loses Heisenberg scaling immediately, while Choi trace norm changes gradually.
Quantum channel tomography learns an unknown process from black-box queries. Earlier work identified a dilation-rate boundary between Heisenberg and classical query scaling, but left the narrow region just beyond that boundary unresolved. This paper supplies matching or optimal bounds there. For diamond-norm error, it finds the Heisenberg advantage disappears as soon as the dilation rate exceeds one. For Choi trace-norm error, the formula instead yields a gradual transition as the rate moves away from the boundary. The result settles asymptotic query complexity under the paper's dimensional and rank assumptions; it is not a performance claim for a particular quantum processor.
Why it matters
New bounds close the near-boundary gap: diamond-norm tomography loses Heisenberg scaling immediately, while Choi trace norm changes gradually.
Limits and context
- The result settles asymptotic query complexity under the paper's dimensional and rank assumptions; it is not a performance claim for a particular quantum processor.
Key claims
New bounds close the near-boundary gap: diamond-norm tomography loses Heisenberg scaling immediately, while Choi trace norm changes gradually.
Qualification: The result settles asymptotic query complexity under the paper's dimensional and rank assumptions; it is not a performance claim for a particular quantum processor.
Evidence: source-2026-11-03-007
Sources
- arXiv preprint 2611.03639, original v1arXiv · primary research
Corrections
No corrections have been recorded for this story.