Experimental demonstration of nonlinear quantum metrology with optimal quantum state

Quantum metrology with precision reaching beyond-$1/N$ scaling through $N$-probe entanglement generating interactions

“…Besides the nonclassical probe states, quantum parameterization processes based on nonlinear interactions between the probes and the to-be-measured (TBM) system, can also improve the precision by amplifying the phase imprinted by the TBM quantity to the probes. For instance, the nonlinear k-body interaction can reach a precision scaling of N −k (N −k+ 1 2 ), with (without) entanglement of the probe [11][12][13][14][15], and the nonlinear N -body entanglement generating interaction can even achieve an exponential Heisenberg limit of 2 −N for measuring its interaction strength [16]. These studies support higher than SQL scaling with N for the precision and are broadly applicable.…”

Generating nonlinearities from conditional linear operations, squeezing and measurement for quantum computation and super-Heisenberg sensing

“…This results in super-Heisenberg scaling for the phase estimations where ∆θ ∼ 1/n 3/2 . Experimentally, super-Heisenberg precision has only been demonstrated using a nonlinear atomic interferometer [43], and using many-body couplings in NMR [26]. Before describing how to achieve super-Heisenberg scaling for phase estimation of an unknown phase θ, using the protocol shown in Fig.…”

“…where F is the classical Fisher information of the distribution of measurement results given by F [{P l }] = l (∂ θ P l ) 2 /P l , ρl = ρl /P l , is the normalized reduced density matrix of the system conditioned on the measurement result l, and F Q , is the single instance QFI given above in (26). Using this form of the QFI, the Cramer Rao bound is given by…”

Floquet-engineered quantum state transfer in spin chains

“…(26) can keep the final states fidelity above 0.996. Then we packed the operator into one shaped pulse calculated by the gradient ascent pulse engineering (GRAPE) method [52][53][54][55], with a duration of 25 ms. The shaped pulse is designed to be robust against the inhomogeneity of the practical control field and has numerical fidelities over 0:995.…”