Characterize the computational boundary for correlated thermal baths

Derive an analogue of the local calibration parameter \(\chi_{\max}\) that characterizes computational simulability and resource generation for general correlated thermal baths, beyond the independent local Markov-bath setting.

Background

The paper establishes an exact computational boundary, expressed through the maximum local parameter $\chi_i=(1-p_e^{(i)})T_2^{(i)}/T_1^{(i)}-1$, for independent local Markov baths. In that setting, nonpositive values at every location guarantee efficient classical simulation of all monitored branches, whereas a positive value at one repeatedly accessible location enables universal quantum computation.

The authors note that correlations between qubits sharing a common thermal bath can generate a positive short-time resource margin even when every local $\chi_i$ is nonpositive. Consequently, the local parameters $T_1$, $T_2$, and $p_e$ do not capture the collective computational resource, motivating a characterization of the appropriate boundary for general correlated baths.