https://doi.org/10.1038/s41467-019-08338-3                            OPEN

                  Author Correction: Narrow bounds for the
                  quantum capacity of thermal attenuators
                  Matteo Rosati               1,2,   Andrea Mari2 & Vittorio Giovannetti2

                  Correction to: Nature Communications; https://doi.org/10.1038/s41467-018-06848-0; published online 18 October 2018

                  The original version of this Article contained an error in Equation (40). The numerator of the fraction inside the logarithm was missing
                  an overall minus sign, and incorrectly read:
                                                                                                             
1234567890():,;




                                                                                              N ð1  ηÞ  η
                                                             Q Φη;N 
 Qtwist ¼ max 0; log2
                                                                                               ð1 þ N Þð1  ηÞ


                  The correct form of Equation (40) is:
                                                                                                                     
                                                                                                          η  N ð1  ηÞ
                                                                           Q Φη;N 
 Qtwist ¼ max 0; log2
                                                                                                         ð1 þ N Þð1  ηÞ


                  This error has been corrected in both the PDF and HTML versions of the Article.




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                  © The Author(s) 2019




                  1 Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain. 2 NEST, Scuola

                  Normale Superiore and Istituto Nanoscienze-CNR, 56127 Pisa, Italy. Correspondence and requests for materials should be addressed to
                  M.R. (email: matteo.rosati@uab.cat)

                  NATURE COMMUNICATIONS | (2019)10:316 | https://doi.org/10.1038/s41467-019-08338-3 | www.nature.com/naturecommunications                                                                 1