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In the information loss problem in black hole evaporation, investigation ofthe purification partner of a Hawking particle is crucial. It is a well-knownfact that 3+1 dimensional spherically symmetric gravitational collapse can beapproximately described by 1+1 dimensional moving mirror models. Since adetected particle in field theory is defined by what a particle detectorobserves, the diversity of detector designs yields a variety of particles andtheir partners. We provide a formula of generalized partners of detectedparticles emitted out of mirrors in arbitrary motion in a free massless scalarfield theory. Using the formula, we directly demonstrate information storageabout pre-thermal information in a pure state of a Hawking particle and itspartner. The partner form drastically changes depending on the detailed designsof particle detectors for the Hawking radiation. In a case of the Hawkingparticle and its partner sensitive to information about pre-thermal era,spatial configurations of the partner has long tails in a stage where onlyzero-point fluctuation is emitted out of the mirror.

Partner formula for an arbitrary moving mirror in $1+1$ dimensions