Variance-Based Sensitivity Analysis of $\mathrm{\Lambda }$-type Quantum Memory

The storage and retrieval of photonic quantum states, quantum memory, is a key resource for a wide range of quantum applications. Here we investigate the sensitivity of $\mathrm{\Lambda }$-type quantum memory to experimental fluctuations and drift. We use a variance-based approach, focusing on the effects of fluctuations and drift on memory efficiency. We consider shot-to-shot fluctuations of the memory parameters, and separately we consider longer timescale drift of the control field parameters. We find the parameters that a quantum memory is most sensitive to depend on the quantum memory protocol being employed, where the observed sensitivity agrees with physical interpretation of the protocols. We also present a general framework that is applicable to other figures of merit beyond memory efficiency. These results have practical ramifications for quantum memory experiments.