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The recovery of fragile quantum states from decoherence is the basis ofbuilding a quantum memory, with applications ranging from quantumcommunications to quantum computing. Many recovery techniques, such as quantumerror correction, rely on the apriori knowledge of the environment noiseparameters to achieve their best performance. However, such parameters arelikely to drift in time in the context of implementing long-time quantummemories. This necessitates using a "spectator" system, which estimates thenoise parameter in real-time, then feed-forwards the outcome to the recoveryprotocol as a classical side-information. The memory qubits and the spectatorsystem hence comprise the building blocks for a real-time (i.e. drift-adapting)quantum memory. In this article, I consider spectator-based (incompleteknowledge) recovery protocols as a real-time parameter estimation problem(generally with nuisance parameters present), followed by the application ofthe "best-guess" recovery map to the memory qubits, as informed by theestimation outcome. I present information-theoretic and metrological bounds onthe performance of this protocol, quantified by the diamond distance betweenthe "best-guess" recovery and optimal recovery outcomes, thereby identifyingthe cost of adaptation in real-time quantum memories. Finally, I providefundamental bounds for multi-cycle recovery in the form of recurrenceinequalities. The latter suggests that incomplete knowledge of the noise couldbe an advantage, as errors from various cycles can cohere. These results areillustrated for the approximate [4,1] code of the amplitude-damping channel andrelations to various fields are discussed.

Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories