Entanglement and quantum information
Can measuring two quantum copies together beat measuring them one by one?
Open access · cc by · source: Europe PMC
Measuring two copies of a noisy qubit jointly with an entangling circuit estimated two rotation angles more precisely than any one-at-a-time measurement can, on real quantum computers.
Study at a glance
- Design
- Other — Theory-designed measurement circuits run on several quantum processors (IBM, Rigetti, trapped-ion, photonic) to estimate two small qubit rotations under controlled decoherence
- N
- No participant sample; each unknown angle was estimated 400 times, each estimate averaging 512 circuit repetitions (341 for three-copy circuits)
- Population
- Qubits on the Fraunhofer IBM Q System One, 11 cloud IBM Q processors, Rigetti Aspen-9, the AQTION trapped-ion processor and the JenQuant photonic processor
- Outcome
- Mean squared error of simultaneous estimates of two rotation angles, compared with Nagaoka and Holevo bounds
Structured fields used in claim comparison tables when every cited study has a complete layer.
Key findings
On the dedicated IBM device, two-copy measurements gave errors 19 ± 4% below the theoretical single-copy limit when averaged over a range of angles, only 6 ± 4% above the ultimate Holevo bound, whereas single-copy measurements must be at least 33% above it. The maximum two-copy advantage across decoherence levels was 21 ± 4%. The trapped-ion and photonic devices reached single-copy limits without mitigation, but Rigetti reached none of the limits and three-copy circuits failed on all devices due to gate errors. Two-copy measurements also violated the Lu–Wang uncertainty relation by more than three standard deviations.
Methodology
The authors considered a qubit rotated by small unknown angles about the x and y axes and then partly decohered, and derived optimal measurements that act on one, two or three copies at once. They compiled these into quantum circuits and ran them on superconducting processors (a dedicated IBM system, cloud IBM machines, Rigetti), a trapped-ion processor and, for single-copy measurements, a photonic processor. A simple calibration-based error mitigation removed constant bias, and the mean squared error of the angle estimates was compared with theoretical bounds.
Limitations
The advantage is shown for a specific toy estimation problem (small rotations of one qubit with a particular noise model), not a practical sensor. Three-copy measurements, which should get closer to the Holevo bound, performed worse in practice because deeper circuits accumulate more errors, so scaling to many copies is unproven. Error mitigation worked best where the team had unrestricted device access, and the photonic device could only do single-copy measurements.
How this study connects
Role on claims
Each row is a claim on a concept or method page where this paper supports, challenges, or qualifies the statement. Roles are hand-checked — not a model guess.
Entanglement gives measurable advantages, in narrow settings.
Entangled probes improve measurements in specific ways: two-photon N00N states doubled the Earth-rotation phase in a fibre Sagnac interferometer (factor 1.96), and two-copy entangling measurements on an IBM device beat the single-copy error limit by 19 ± 4%.
Evidence for the claim as stated.
Scaling fails in practice: three-copy measurements performed worse than two-copy because of gate errors, and N00N states lost about 99% of pairs to loss, so advantages shown with two copies or two photons may not grow with size.
Evidence for the claim as stated.
Circuit depth is limited by accumulated gate error.
Current processors already support physics experiments but are limited by gate errors: scar-state revivals on a superconducting ladder decayed due to device imperfections, and three-copy measurement circuits failed on all tested devices.
Evidence for the claim as stated.
Open questions
Tensions this paper is part of
From concept pages' “where studies disagree.” Disagreement means the same question; scope means different assays, populations, or outcomes.
Scaling fails in practice: three-copy measurements performed worse than two-copy because of gate errors, and N00N states lost about 99% of pairs to loss, so advantages shown with two copies or two photons may not grow with size.
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