Many-copy formation and regularization of the noisy fermionic family

Determine the formation values at blocklengths greater than two and the regularized formation value for the noisy two-mode fermionic Gaussian family \(\tau_t=\frac14(1-t\gamma_2\gamma_3)\) with \(0<t<1\), in order to characterize how optimal collective preparation changes away from the state \(\tau\).

Background

The paper exactly determines the one-copy and two-copy physical and Gaussian entanglement-of-formation values for the noisy family $\tau_t$, and proves strict two-copy nonadditivity for every $t>0$, including the full-rank regime $0$\tau_t$ is also unresolved. Resolving these quantities would establish how the collective-preparation advantage found for the endpoint state $\tau$ changes under noise.