  In this work we probe the impact of channel estimation on the performance of
quantum LDPC codes. Our channel estimation is based on an optimal estimate of
the relevant decoherence parameter via its quantum Fisher information. Using
state-of-the art quantum LDPC codes designed for the quantum depolarization
channel, and utilizing various quantum probes with different entanglement
properties, we show how the performance of such codes can deteriorate by an
order of magnitude when optimal channel identification is fed into a belief
propagation decoding algorithm. Our work highlights the importance in quantum
communications of a viable channel identification campaign prior to decoding,
and highlights the trade-off between entanglement consumption and quantum LDPC
code performance.
