Approximate quantum encryption with faster key expansion

Perfect encryption of a qubit state using the Quantum One-Time Pad (QOTP) requires 2 classical key bits. More generally, perfect encryption of a 2n-dimensional state requires 2n classical bits. However, almost-perfect encryption, with information-theoretic security, can be achieved with only little more than 1 key bit per qubit. It has been shown that key length n+2log1/ε suffices to encrypt n qubits in such a way that the cipherstate has trace distance ≤ε from the fully mixed state. In this paper, we present a fast key expansion method to create a 2n-bit pseudorandom string which is then used as a QOTP key. In this expansion we make use of 2n bits of public randomness which are included as a classical part of the cipherstate. Our key expansion is a factor 2 faster than the previous fastest scheme, while achieving the shortest known key length n+2log1/ε.