Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).
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New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.
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Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).
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Quantum metrology of mixed states via purification
New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.