Quantum trajectory of a spin oscillator, continuous retrodiction beyond the Heisenberg uncertainty relation
Abstract
The Heisenberg uncertainty relation in quantum mechanics limits the precision of predicting the outcome of measurements of any non-commuting observables. However, this restriction does not apply to retrodictive guessing of the outcomes of past measurements. Here, we experimentally demonstrate this using a spin oscillator consisting of $ 5.17 \times 10^{10}$ rubidium atoms. Through weak continuous measurements, we monitor canonical spin observables x̂A and p̂A with [x̂A,p̂A] = iℏ. By combining information obtained before and after time t, we retrodict the outcomes of measurements of x̂A and p̂A at time t with variances that remain, concurrently over 1.4 hours, ∼ 1.01 dB below the bound set by the Heisenberg uncertainty relation. We also infer and demonstrate the ability to retrodict, with the same precision, the measurement outcomes for arbitrary quadratures of the spin oscillator. This brings interesting prospects for further research on quantum measurements, and for quantum-enhanced sensing that combines trajectory and entanglement strategies.
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BibTeX
@misc{li2026quantum,
title = {{Quantum trajectory of a spin oscillator, continuous retrodiction beyond the Heisenberg uncertainty relation}},
author = {Peiying Li and Junlei Duan and Suotang Jia and Klaus Mølmer and Yanhong Xiao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08104},
eprint = {2611.08104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08104},
}
RIS
TY - UNPB
TI - Quantum trajectory of a spin oscillator, continuous retrodiction beyond the Heisenberg uncertainty relation
AU - Peiying Li
AU - Junlei Duan
AU - Suotang Jia
AU - Klaus Mølmer
AU - Yanhong Xiao
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08104
UR - https://arxiv.org/abs/2611.08104
AB - The Heisenberg uncertainty relation in quantum mechanics limits the precision of predicting the outcome of measurements of any non-commuting observables. However, this restriction does not apply to retrodictive guessing of the outcomes of past measurements. Here, we experimentally demonstrate this using a spin oscillator consisting of $ 5.17 \times 10^{10}$ rubidium atoms. Through weak continuous measurements, we monitor canonical spin observables x̂_A and p̂_A with [x̂_A,p̂_A] = iℏ. By combining information obtained before and after time t, we retrodict the outcomes of measurements of x̂_A and p̂_A at time t with variances that remain, concurrently over 1.4 hours, ∼ 1.01 dB below the bound set by the Heisenberg uncertainty relation. We also infer and demonstrate the ability to retrodict, with the same precision, the measurement outcomes for arbitrary quadratures of the spin oscillator. This brings interesting prospects for further research on quantum measurements, and for quantum-enhanced sensing that combines trajectory and entanglement strategies.
ER -