We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin 3/2 interacting with a global bosonic environment. We make use of an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare the dynamical effects due to decoherence with those that arise in a pair of distinguishable qubits immersed in the same environment. According to the system’s initial state, three types of qualitatively different dynamics are identified: i) invariant regime , corresponding to initial states that belong to a decoherence free subspace (DFS), which maintain invariant their entanglement and coherence throughout the evolution; ii) exponential decay , corresponding to initial states orthogonal to the DFS, and evolve towards states whose entanglement and coherence decrease exponentially; iii) entanglement sudden death , corresponding to initial states that have some overlap with the DFS and exhibit a richer dynamics leading, in particular, to the sudden death of the fermionic entanglement, while the coherence decays exponentially. Our analysis offers insights into the dynamics of entanglement in open systems of identical particles and into the existence of decoherence free subspaces and entanglement sudden death in indistinguishable-fermion systems.

The conventional certification method for quantum teleportation protocols relies on surpassing the highest achievable classical average fidelity between target and teleported states. Our paper highlights the limitations of this approach: inconsistent conclusions can be obtained when considering different distance measures in the quantum state space, leading to contradictory interpretations. In particular, this behavior is manifested when modeling a very common noisy experimental scenario, in which the resource state takes the form of a Werner state generated by the influence of a depolarizing channel acting on the Bell state resource. Two additional noise models, based on amplitude-damping channels, are also analyzed. Our paper, therefore, stresses the necessity of new certification methods for quantum teleportation.

We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are the transmission distance between quantum channels and the entropic channel divergence. We investigate their mathematical properties and discuss their physical meaning. Additionally, we establish a chain rule for the entropic channel divergence, which implies the amortization collapse, a relevant result with potential applications in the field of discrimination of quantum channels and converse bounds. Finally, we analyze the distinguishability between two given Pauli channels and study exemplary Hamiltonian dynamics under decoherence.

We demonstrate that, among all quantum teleportation protocols giving rise to the same average fidelity, those with aligned Bloch vectors between the input and output states exhibit the minimum average trace distance. This defines optimal protocols. Furthermore, we show that optimal protocols can be interpreted as the perfect quantum teleportation protocol under the action of correlated one-qubit channels. In particular, we focus on the deterministic case for which the final Bloch vector length is equal for all measurement outcomes. Within these protocols, there exists one type that corresponds to the action of uncorrelated channels: these are depolarizing channels. Thus, we established the optimal quantum teleportation protocol under a very common experimental noise.