PnrArray

Multiplexed threshold array: POVM, threshold limit, PNR limit

11/11 passed in 72ms

Test	What it does	Result
test_array_click	At one element the array POVM reproduces click_prob across efficiency, dark count and coherent-state flux.	✅ pass
test_array_coherent	Folding the POVM against a Poisson photon-number distribution agrees with the closed binomial count a balanced splitter gives directly.	✅ pass
test_array_complete	The array's elements sum to the identity on the truncated space and each one is positive semi-definite.	✅ pass
test_array_converge	Doubling the element count halves the deficit from true photon-number resolution, which is first order in 1/N with coefficient $n(n-1)/2$.	✅ pass
test_array_dark	On vacuum the array reports a binomial count over its elements.	✅ pass
test_array_distinct	At unit efficiency the probability of reporting the true number is exactly pnr_distinct, the probability that no two photons share a bin.	✅ pass
test_array_efficiency	The no-click probability falls monotonically with element efficiency and is exactly zero at unit efficiency on three photons.	✅ pass
test_array_elements	The probability of reporting the true photon number rises monotonically with the element count, at fixed per-element efficiency.	✅ pass
test_array_inclusion	The occupancy recursion agrees with the closed inclusion-exclusion form of the same POVM, evaluated in exact rationals.	✅ pass
test_array_threshold	At one element the no-click element is (1 - d)(1 - eta)^n on the Fock diagonal.	✅ pass
test_array_vacuum	The no-click element is (1 - d)^N (1 - eta)^n at every element count.	✅ pass