  We present a scheme for hiding bits in Bell states that is secure even when
the sharers Alice and Bob are allowed to carry out local quantum operations and
classical communication. We prove that the information that Alice and Bob can
gain about a hidden bit is exponentially small in $n$, the number of qubits in
each share, and can be made arbitrarily small for hiding multiple bits. We
indicate an alternative efficient low-entanglement method for preparing the
shared quantum states. We discuss how our scheme can be implemented using
present-day quantum optics.
