On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3 ⊗ 3 and 4 ⊗ 4 systems are constructed. In both cases, the constructed EWs correspond to the hyperplanes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).

In this paper, we introduce a new alternative quantum fidelity for quantum states which perfectly satisfies all Jozsa's axioms and is zero for orthogonal states. By employing this fidelity, we derive an improved bound for quantum speed limit time in open quantum systems in which the initial states can be chosen as either pure or mixed. This bound leads to the well-known Mandelstamm-Tamm type bound for nonunitary dynamics in the case of initial pure states. However, in the case of initial mixed states, the bound provided by the introduced fidelity is tighter and sharper than the obtained bounds in the previous works.

In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the limit t → ∞, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additional qubits in each reservoir, the initial coherence and the respective entanglements are completely protected in both Markovian and non-Markovian regimes. Interestingly, the protection of entanglements occurs even under the individually different behaviors of the reservoirs.