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Quantum entropic security and approximate quantum encryption

An approximate quantum encryption scheme uses a private classical key to encrypt a quantum state while leaking only a very small amount of information to the adversary. Previous work has shown that while we need 2n bits of key to encrypt n qubits exactly, we can get away with only n bits in the approximate case, provided that we know that the state to be encrypted is not entangled with something that the adversary already has in his possession. In this talk, I will show a generalisation of this result: approximate quantum encryption requires roughly n-t bits of key, where t is a lower bound on the quantum conditional min-entropy of the state to be encrypted given the adversary's prior knowledge. I will show that this result follows naturally from a quantum version of entropic security and indistinguishability. This is joint work with Simon-Pierre Desrosiers.