  If a quantum system is subject to noise, it is possible to perform quantum
error correction reversing the action of the noise if and only if no
information about the system's quantum state leaks to the environment. In this
article, we develop an analogous duality in the case that the environment
approximately forgets the identity of the quantum state, a weaker condition
satisfied by epsilon-randomizing maps and approximate unitary designs.
Specifically, we show that the environment approximately forgets quantum states
if and only if the original channel approximately preserves pairwise fidelities
of pure inputs, an observation we call weak decoupling duality. Using this
tool, we then go on to study the task of using the output of a channel to
simulate restricted classes of measurements on a space of input states. The
case of simulating measurements that test whether the input state is an
arbitrary pure state is known as equality testing or quantum identification. An
immediate consequence of weak decoupling duality is that the ability to perform
quantum identification cannot be cloned. We furthermore establish that the
optimal amortized rate at which quantum states can be identified through a
noisy quantum channel is equal to the entanglement-assisted classical capacity
of the channel, despite the fact that the task is quantum, not classical, and
entanglement-assistance is not allowed. In particular, this rate is strictly
positive for every non-constant quantum channel, including classical channels.
