Closed-form second moments for generic bosonic observables and anti-concentration of Fock-state probabilities established in boson sampling for the saturated regime where mode number grows linearly with photon number.
Indeed, PaleyβZygmund yields Pr πβΌπ(π) πβΌΞ¦π π ππ(π)β©ΎπΌ |Ξ¦π π| β©Ύ (1βπΌ)2 π2(π, π),(E14) as detailed in the proof of Corollary 1
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Boson sampling beyond the dilute regime: second moments and anti-concentration
Closed-form second moments for generic bosonic observables and anti-concentration of Fock-state probabilities established in boson sampling for the saturated regime where mode number grows linearly with photon number.