  The locking effect is a phenomenon which is unique to quantum information
theory and represents one of the strongest separations between the classical
and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking
protocol harnesses this effect in a cryptographic context, whereby one party
can encode n bits into n qubits while using only a constant-size secret key.
The encoded message is then secure against any measurement that an eavesdropper
could perform in an attempt to recover the message, but the protocol does not
necessarily meet the composability requirements needed in quantum key
distribution applications. In any case, the locking effect represents an
extreme violation of Shannon's classical theorem, which states that
information-theoretic security holds in the classical case if and only if the
secret key is the same size as the message. Given this intriguing phenomenon,
it is of practical interest to study the effect in the presence of noise, which
can occur in the systems of both the legitimate receiver and the eavesdropper.
This paper formally defines the locking capacity of a quantum channel as the
maximum amount of locked information that can be reliably transmitted to a
legitimate receiver by exploiting many independent uses of a quantum channel
and an amount of secret key sublinear in the number of channel uses. We provide
general operational bounds on the locking capacity in terms of other well-known
capacities from quantum Shannon theory. We also study the important case of
bosonic channels, finding limitations on these channels' locking capacity when
coherent-state encodings are employed and particular locking protocols for
these channels that might be physically implementable.
