a wound, cells crossing a developing embryo, and cancerous cells migrating from tumors. Chemotaxis, sensing and responding to chemical gradients, is crucial in all of these examples [@swaney2010eukaryotic; @levine2013physics]. Chemotaxis is traditionally studied by exposing single cells to gradients – but cells often travel in groups, not singly [@hakim2017collective; @camley2017physical]. Collective cell migration is essential to development and metastasis [@friedl2009collective], and can have remarkable effects on chemotaxis. Even when single cells cannot sense a gradient, a cluster of cells may cooperate to sense it. While collective chemotaxis is our primary focus, this “emergent” gradient sensing is found in response to many signals, including soluble chemical gradients (chemotaxis) [@theveneau2010collective; @malet2015collective; @ellison2016cell], conditioned substrates (haptotaxis) [@winklbauer1992cell], substrate stiffness gradients (durotaxis) [@sunyer2016collective] and electrical potential (galvanotaxis) [@li2012cadherin; @lalli2015collective].

Cells can cooperate to sense gradients – but the physical principles limiting a cluster’s sensing accuracy are not settled. For single cells, the fundamental bounds on sensing chemical concentrations and gradients are well-studied [@berg1977physics; @kaizu2014berg; @hu2010physical; @hu2011geometry; @endres2009maximum; @endres2008accuracy; @fuller2010external; @ueda2007stochastic; @andrews2007information; @bialek2005physical], showing unavoidable stochasticity in receptor-ligand binding limits chemotactic accuracy. Is this true for cell clusters? Is a cell cluster simply equivalent to a larger cell? No! There is an essential difference between 