Under the multispecies coalescent model of molecular evolution, gene trees have independent evolutionary histories within a shared species tree. In comparison, supermatrix concatenation methods assume that gene trees share a single common genealogical history, thereby equating gene coalescence with species divergence. The multispecies coalescent is supported by previous studies which found that its predicted distributions fit empirical data, and that concatenation is not a consistent estimator of the species tree. *BEAST, a fully Bayesian implementation of the multispecies coalescent, is popular but computationally intensive, so the increasing size of phylogenetic data sets is both a computational challenge and an opportunity for better systematics. Using simulation studies, we characterize the scaling behaviour of *BEAST, and enable quantitative prediction of the impact increasing the number of loci has on both computational performance and statistical accuracy. Follow up simulations over a wide range of parameters show that the statistical performance of *BEAST relative to concatenation improves both as branch length is reduced and as the number of loci is increased. Finally, using simulations based on estimated parameters from two phylogenomic data sets, we compare the performance of a range of species tree and concatenation methods to show that using *BEAST with tens of loci can be preferable to using concatenation with thousands of loci. Our results provide insight into the practicalities of Bayesian species tree estimation, the number of loci required to obtain a given level of accuracy and the situations in which supermatrix or summary methods will be outperformed by the fully Bayesian multispecies coalescent.
We derive a formalism of stochastic master equations (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak quantum measurement (weak spectroscopy). On account of that correlated environments can lead to a nonlocal open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.
It has been found that the quantum-to-classical transition can be observed independent of macroscopicity of the quantum state for a fixed degree of fuzziness in the coarsened references of measurements. Here, a general situation, that is the degree of fuzziness can change with the rotation angle between two states (different rotation angles represent different references), is researched based on the reason that the fuzziness of reference can come from two kinds: the Hamiltonian (rotation frequency) and the timing (rotation time). Our results show that, for the fuzziness of Hamiltonian alone, the degree of fuzziness for reference will change with the rotation angle between two states and the quantum effects can still be observed no matter how much degree of fuzziness of Hamiltonian; for the fuzziness of timing, the degree of coarsening reference is unchanged with the rotation angle. Moreover, during the rotation of the measurement axis, the decoherence environment can also help the classical-to-quantum transition due to changing the direction of measurement axis.
We propose a new scheme to generate the multi-photon entanglement via two steps, that is, first to utilize the superconductor to create the multi-quantum-dot entanglement, and then to use the input photon to transfer it into the multi-photon entanglement. Moreover, the maximum probability for the swap of photon and quantum-dot qubits is close to unit for a single input Gaussian photon. More importantly, by mapping the multi-quantum-dot state into the coherent states of oscillators, such as cavity modes, the multi-quantum-dot entanglement in our scheme can be protected from the decoherence induced by the noise. Thus, it is possible to generate more than eight spatially separated entangled photons in the realistic experimental conditions.
