# Unifying classical and quantum key distillation

## Matthias Christandl and Artur Ekert and Michal Horodecki and Pawel Horodecki and Jonathan Oppenheim and Renato Renner

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```Assume that two distant parties, Alice and Bob, as well as an
adversary, Eve, have access to (quantum) systems prepared jointly
according to a tripartite state. In addition, Alice and Bob can
use local operations and authenticated public classical
communication. Their goal is to establish a key which is unknown to
Eve. We initiate the study of this scenario as a unification of two
standard scenarios: (i) key distillation (agreement) from classical
correlations and (ii) key distillation from pure tripartite quantum
states.
Firstly, we obtain generalisations of fundamental results related to
scenarios (i) and (ii), including upper bounds on the key rate,
i.e., the number of key bits that can be extracted per copy of
the initial state. Moreover, based on an embedding of classical
distributions into quantum states, we are able to find new
connections between protocols and quantities in the standard
scenarios (i) and (ii).
Secondly, we study specific properties of key distillation
protocols. In particular, we show that every protocol that makes
use of pre-shared key can be transformed into an equally efficient
protocol which needs no pre-shared key. This result is of practical
significance as it applies to quantum key distribution (QKD)
protocols, but it also implies that the key rate cannot be locked
with information on Eve's side. Finally, we exhibit an arbitrarily
large separation between the key rate in the standard setting where
Eve is equipped with quantum memory and the key rate in a setting
where Eve is only given classical memory. This shows that
assumptions on the nature of Eve's memory are important in order to
determine the correct security threshold in QKD.