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The design of error-correcting codes used in modern communications relies oninformation theory to quantify the capacity of a noisy channel to sendinformation [1]. This capacity can be expressed using the mutual informationbetween input and output for a single use of the channel: although correlationsbetween subsequent input bits are used to correct errors, they cannot increasethe capacity. For quantum channels, it has been an open question whetherentangled input states can increase the capacity to send classical information[2]. The additivity conjecture [3,4] states that entanglement does not help,making practical computations of the capacity possible. While additivity iswidely believed to be true, there is no proof. Here we show that additivity isfalse, by constructing a random counter-example. Our results show that the mostbasic question of classical capacity of a quantum channel remains open, withfurther work needed to determine in which other situations entanglement canboost capacity.

Superadditivity of communication capacity using entangled inputs