Bosonic and fermionic many-body interference probabilities with partial distinguishability obey a complementarity identity whose correlation matrices sum to twice the classical case, constraining metrology sensitivity.
The symmetric characteristic function is defined as follows: χρ (ααα) =Tr(D(ααα)ρ).(59) We will exploit two facts:
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Complementarity between bosonic and fermionic many-body interferences with partially distinguishable particles
Bosonic and fermionic many-body interference probabilities with partial distinguishability obey a complementarity identity whose correlation matrices sum to twice the classical case, constraining metrology sensitivity.