Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical processes aided by enzymes. Performance of these enzymes is usually characterized in terms of their average error rate and speed. However, because of thermal fluctuations in these single-molecule processes, both error and speed are inherently stochastic quantities. In this paper, we study fluctuations of error and speed in biopolymer synthesis and show that they are in general correlated. This means that, under equal conditions, polymers that are synthesized faster due to a fluctuation tend to have either better or worse errors than the average. The error-correction mechanism implemented by the enzyme determines which of the two cases holds. For example, discrimination in the forward reaction rates tends to grant smaller errors to polymers with faster synthesis. The opposite occurs for discrimination in monomer rejection rates. Our results provide an experimentally feasible way to identify error-correction mechanisms by measuring the error-speed correlations.Organisms encode genetic information in heteropolymers such as DNA and RNA. Replication of these heteropolymers is a non-equilibrium process catalyzed by enzymes. The crucial observables to characterize these enzymes are their error rate and speed. A low error, defined as the fraction of monomers in the copy that do not match the template, ensures correct trasmission of biological information. High processing speed is also crucial to guarantee fast cell growth. Theoretical approaches have been developed to compute the average error and average speed of polymerization processes [1][2][3][4][5][6][7]. However, at the single molecule level, both error and speed can present significant stochastic fluctuations.In this Letter we address fluctuations in the error and speed of polymer synthesis. In particular, we show that correlations between these quantities exist. These correlations provide a way to identify the error correction mechanism adopted by an enzyme from experimental data. This approach can circumvent the characterization of these enzymes by measuring all kinetic rates of the underlying reaction network [8][9][10][11][12][13][14][15].We consider an enzyme that replicates an existing template polymer by sequentially incorporating monomers into a copy polymer (Figure 1a). In a given time interval T , the enzyme synthesizes a copy made up of a number of monomers L. Because of thermal fluctuations, enzymes sometimes incorporate wrong monomers (w) that do not match the template, instead of the right ones (r). In practical cases, there can be multiple types of wrong monomers; for simplicity, we do not distinguish among them. We denote R as the number of right matches and W the number of wrong matches in the copy, so that R + W = L. The error of the polymer copy can be then expressed asWe focus on two possible setups, corresponding to two idealized experiments. In the first, the enzyme replicates a given template polymer for a fixed time T ≫ 1. (Fig. 1b). Due to the stochasticity of single-...