B92Tamaki

The Tamaki-Lutkenhaus bound: a derived phase error and the published thresholds

7/7 passed in 465ms

Test	What it does	Result
test_channel_form	The depolarising channel gives the conclusive rate and bit error the Bloch-shrinking factor predicts.	✅ pass
test_depol_limit	The tolerable depolarising rate reproduces Tamaki and Lutkenhaus's three values, at an optimum overlap reported as the amplitude whose square their Fig. 2(b) plots.	✅ pass
test_error_tolerance	The bit error tolerated at those thresholds sits under the Shor-Preskill 11.00%.	✅ pass
test_phase_rises	The derived phase error rises with channel loss and with the bit error rate, and saturates at 1/2.	✅ pass
test_plain_derived	The end-to-end plain rate agrees with the gain, bit error and phase error it derives, and reaches zero past the depolarising threshold.	✅ pass
test_special_case	The solved phase bound reproduces the paper's closed zero-bit-error special case over the stated overlap and loss ranges.	✅ pass
test_usd_boundary	The phase bound reaches exactly 1/2 at loss L = c, where unambiguous discrimination takes the protocol over.	✅ pass