(the stimulated emission state signal) with the focusing scheme can be found in Fig. of Ref. 8. The condition in Eq. 28 is typically searched by enumerating all possible K = {a, b} and then performing the search over O(K 2 ) elements. To compute μρ , one in principle will need to multiply two O(K 2 ) size matrices. Furthermore, from Eq. 26, in order to calculate the CDF of this large matrix, we need to perform another O(K 2 ) operation on μρ . This is a challenging task for computing polariton spectra under the collective coupling regime, with respect to both time and memory requirements as K ∝ N 2 , especially with a large N .