For a mixed Gaussian probe, the post-selected quantum Fisher information grows with temperature and can surpass the non-post-selected strategy, while the signal-to-noise improvement is bounded by weak-measurement validity.
Complete description of a quantum system at a given time.Journal of Physics A: Mathematical and General, 24(10):2315, 1991
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Temperature-induced measurement sensitivity enhancement via imaginary weak values
For a mixed Gaussian probe, the post-selected quantum Fisher information grows with temperature and can surpass the non-post-selected strategy, while the signal-to-noise improvement is bounded by weak-measurement validity.