Quantum / CONCEPT

Cat pairs need not be optimal for metrology with noisy measurements

Len, Gefen, Retzker and Kołodyński (arXiv:2109.01160, Nature Communications 13, 6971) conjecture that for every classical noise channel M_x = sum_i p(x|i) Pi_i applied independently to N probes, the pair of orthonormal states maximizing the noisy Fisher coefficient gamma can be taken of cat form cos(theta)|j>^N + sin(theta)|k>^N, -sin(theta)|j>^N + cos(theta)|k>^N. For a three-outcome qutrit detector with entries in (1/20)Z and two probes, the pair |10>, |21> attains a larger gamma than every cat pair.