Sisi Zhou

The Heisenberg limit (HL, with estimation error scales as 1/n) and the standard quantum limit (SQL, 1/sqrt(n)) are two fundamental limits in estimating an unknown parameter in n copies of quantum channels and are achievable with full quantum controls, e.g., quantum error correction (QEC). It is unknown though, whether these limits are still achievable in restricted quantum devices when QEC is unavailable, e.g., with only unitary controls or bounded system sizes. In this talk, I will discuss various new limits for estimating qubit channels under restrictive controls. The HL is proven to be unachievable in various cases, indicating the necessity of QEC in achieving the HL. Furthermore, a necessary and sufficient condition to achieve the SQL is determined, where a novel unitary control protocol is identified to achieve the SQL for certain types of noisy channels, and a constant floor on the estimation error is proven for other cases.

Abstract The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. In quantum metrology, people are interested in calculating the QFI of N identical copies of a quantum channel when N\rightarrow\infty, which we call the asymptotic QFI. It was known that the asymptotic QFI grows either linearly or quadratically with N. Here we obtain a simple criterion that determines whether the scaling is linear or quadratic. In both cases, the asymptotic QFI and a quantum error correction protocol to achieve it are solvable via a semidefinite program. When the scaling is quadratic, the Heisenberg limit, a feature of noiseless quantum channels, is recovered. When the scaling is linear, we show the asymptotic QFI is still in general larger than N times the single-channel QFI and furthermore, sequential estimation strategies provide no advantage over parallel ones. For details, see arXiv: 2003.10559.