Fibroblast growth factor 4 (FGF-4) has been shown to be a signaling molecule whose expression is essential for postimplantation mouse development and, at later embryonic stages, for limb patterning and growth. The FGF-4 gene is expressed in the blastocyst inner cell mass and later in distinct embryonic tissues but is transcriptionally silent in the adult. In tissue culture FGF-4 expression is restricted to undifferentiated embryonic stem (ES) cells and embryonal carcinoma (EC) cell lines. Previously, we determined that EC cell-specific transcriptional activation of the FGF-4 gene depends on a synergistic interaction between octamer-binding proteins and an EC-specific factor, Fx, that bind adjacent sites on the FGF-4 enhancer. Through the cloning and characterization of an F9 cell cDNA we now show that the latter activity is Sox2, a member of the Sry-related Sox factors family. Sox2 can form a ternary complex with either the ubiquitous Oct-1 or the embryonic-specific Oct-3 protein on FGF-4 enhancer DNA sequences. However, only the Sox2/Oct-3 complex is able to promote transcriptional activation. These findings identify FGF-4 as the first known embryonic target gene for Oct-3 and for any of the Sox factors, and offer insights into the mechanisms of selective gene activation by Sox and octamer-binding proteins during embryogenesis.

Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér–Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.

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Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

Time is a valuable resource and it seems intuitive that longer time should lead to better precision in Hamiltonian parameter estimation. However recent studies have put this intuition into question, showing longer time may even lead to worse estimation in certain cases. Here we show that the intuition can be restored if coherent feedback controls are included. By deriving asymptotically optimal feedback controls we present a quantification of the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit of Hamiltonian parameter estimation under the optimal feedback scheme.The implementation of quantum technology usually requires a full and precise information about the parameters of system evolution, which makes quantum Hamiltonian parameter estimation a crucial problem. An important task of Hamiltonian parameter estimation is to find out the ultimate achievable precision limit with given resources and design schemes that attain it. Typically Hamiltonian parameter estimation is achieved by preparing some initial quantum state ρ 0 and letting it evolve under the Hamiltonian H(x), through the evo-−iH(x)T , the unknown parameter in the Hamiltonian is imprinted on ρ x , one then can estimate the parameter by measuring ρ x . This problem is well studied in quantum metrology when the Hamiltonian is in the multiplication form of the parameter H(x) = xH, it is known that in this case the optimal strategy is to prepare the initial state as, where |λ max(min) is the eigenvector of H for the maximum(minimum) eigenvalue, the standard deviation of the optimal unbiased estimator of x then scales as, here n is the number that the process is repeated and J = (λ max −λ min ) 2 T 2 is the maximal quantum Fisher information, where λ max(min) is the maximum(minimum) eigenvalue of H and T is the time that the Hamiltonian acts on initial states [1]. In this case the standard deviation of the estimation scales as In this article, we will show that the intuition can be restored when we include feedback controls. By presenting an asymptotically optimal feedback scheme for general Hamiltonian parameter estimation, we give a quantification of the maximal improvement feedback controls can provide in Hamiltonian parameter estimation. We show that under the optimal scheme the precision limit displays a universal time scaling 1 T which is independent of the form of the Hamiltonian. In this article we focus on single parameter estimation, generalization to multiple parameters is possible but is beyond the scope of this article.The methods developed previously in [3,4] to compute maximal quantum Fisher information for general Hamiltonians are quite invovled and hard to incorporate feedback controls. Here we use a tool developed in our recent work which is computationally efficient and convenient to include feedback controls, which we recapture here briefly [5].