The presence of electrocatalysis in lithium-sulfur batteries has been proposed but not yet sufficiently verified. In this study,m olybdenum phosphide (MoP) nanoparticles are shown to play ad efinitive electrocatalytic role for the sulfur cathode working under lean electrolyte conditions featuring alow electrolyte/active material ratio:the overpotentials for the charging and discharging reactions are greatly decreased. As aresult, sulfur electrodes containing MoP nanoparticles show faster kinetics and more reversible conversion of sulfur species, leading to improvements in charging/discharging voltage profiles,c apacity,r ate performance,a nd cycling stability. Taking advantage of the electrocatalytic properties of MoP, high-performance sulfur electrodes were successfully realized that are steadily cyclable at ah igh areal capacity of 5.0 mAh cm À2 with ac hallenging electrolyte/sulfur (E/S) ratio of 4 mL E mg À1 S .Lithium sulfur batteries (LSBs) have as uperior theoretical specific energy of 2600 Wh kg À1 ,b ut an unsatisfactory cycle life. [1] Thecathode material of LSBs,namely sulfur,islimited in cycling stability,d espite its high theoretical specific capacity of 1675 mAh g À1 . [2] Thec apacity decay is tightly associated with the dissolution and diffusion of lithium polysulfide (LPS) intermediates in the electrolyte,w hich on the one hand facilitates the kinetics of electrochemical conversion [3] but on the other hand causes loss of active material and side reactions. [4] Using polar material surfaces, for example,f unctionalized carbons, [5] metal oxides, [6] sulfides, [7] phosphides, [8] nitrides, [9] and metal-organic frameworks, [10] to confine LPS via chemical interactions has been found to be one of the most effective ways for improving the cycling stability of sulfur electrodes.B esides immobilizing LPS on the cathode,i ti sa lso crucial to ensure their rapid electrochemical conversion and thus capacity contribution. Fori nstance,w eh ave recently reported on molybdenum phosphide (MoP) nanoparticles serving an electrocatalystlike function for stabilizing the sulfur cathode. [8b] While the extension of cycle life was significant, electrocatalysis was only preliminarily implied by the larger cyclic voltammetry current on the MoP-modified electrode in aL PS electrolyte. Herein, we report anew observation of akey evidence for the electrocatalytic role played by MoP nanoparticles in LSBs:reduction of overpotential for the charging/discharging reactions of the sulfur cathode,w hich is only obvious under lean electrolyte conditions (that is,w ith al ow electrolyte/ active material ratio). Fora no rdinary sulfur electrode,t he average charging/discharging voltage hysteresis at ac urrent density of 0.8 mA cm À2 increases greatly to 0.43 Vw hen the electrolyte/sulfur (E/S; mL E mg À1 S )ratio is lowered to 6. With MoP nanoparticles incorporated in the electrode structure, the voltage hysteresis is reduced to 0.18 V. MoP effectively catalyzes the electrochemical conversion reactions of sulfur, which helps the...

No process in nature can perfectly clone an arbitrary quantum state. But is it possible to engineer processes that replicate quantum information with vanishingly small error? Here we demonstrate the possibility of probabilistic super-replication phenomena where N equally prepared quantum clocks are transformed into a much larger number of M nearly perfect replicas, with an error that rapidly vanishes whenever M is small compared with N 2 . The quadratic replication rate is the ultimate limit imposed by quantum mechanics to the proliferation of information and is fundamentally linked with the Heisenberg limit of quantum metrology.

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator's deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, called D-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.