Position and momentum can be jointly localized with probability ≥50% using new confidence uncertainty measures, with explicit lower bounds derived for θ_x + θ_p >1 via projection and operator-norm inequalities.
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Uncertainty-disturbance relations are derived showing uncertainty prerequisites and upper-bounds disturbance, with applications to estimating quantum resources for rank-one projective measurements.
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Confidence uncertainty: position and momentum can be jointly determined with a guaranteed probability
Position and momentum can be jointly localized with probability ≥50% using new confidence uncertainty measures, with explicit lower bounds derived for θ_x + θ_p >1 via projection and operator-norm inequalities.
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Uncertainty-disturbance relations and applications
Uncertainty-disturbance relations are derived showing uncertainty prerequisites and upper-bounds disturbance, with applications to estimating quantum resources for rank-one projective measurements.