  We propose a quantum key distribution (QKD) protocol that is carried out in
an indefinite causal order (ICO). In QKD, one considers a setup in which two
parties, Alice and Bob, share a key with one another in such a way that they
can detect whether an eavesdropper, Eve, has learnt anything about the key. To
our knowledge, in all QKD protocols proposed until now, Eve is detected by
publicly comparing a subset of Alice and Bob's key and checking for errors.
With the use of ICO, we show that it is possible to detect Eve without publicly
comparing any information about the key. Indeed, we prove that both correlated
and uncorrelated eavesdroppers cannot extract any useful information about the
shared key without inducing a nonzero probability of being detected. We discuss
the practicality and implementability of such a protocol and propose an
experimental setup to simulate some of the results derived.
