Hiding bits in Bell states

We present a scheme for secretly sharing bits in Bell states which 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 low-entanglement method for preparing the shared quantum states.