Kavli Affiliate: Jia Liu
| First 5 Authors: Tengyu Ai, Qi Bi, Yuxin He, Jia Liu, Xiao-Ping Wang
| Summary:
We investigate whether collider experiments can reach the quantum limit of
precision, defined by the quantum Fisher information (QFI), using only
classical observables such as particle momenta. As a case study, we focus on
the $tau^+tau^-$ system and the decay channel $tau to pi nu$, which
offers maximal spin-analyzing power and renders the decay a projective
measurement. We develop a general framework to determine when collider
measurements can, in principle, saturate the QFI in an entangled biparticle
system, and this framework extends naturally to other such systems. Within this
framework, QFI saturation occurs if and only if the symmetric logarithmic
derivative (SLD) commutes with a complete set of orthonormal separable
projectors associated with collider-accessible measurements. This separability
condition, reflecting the independence of decay amplitudes, is highly
nontrivial. To meet this condition, a key requirement is that the spin density
matrix be rank-deficient, allowing the SLD sufficient freedom. We show that the
classical Fisher information asymptotically saturates the QFI for magnetic
dipole moments and CP-violating Higgs interactions in selected phase-space
regions, but not for electric dipole moments. These results bridge quantum
metrology and collider physics, providing a systematic method to identify
quantum-optimal sensitivity in collider experiments.
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