The Dynamics of Quantumness in the Bloch Channels with the Indefinite Causal Order

The dynamics of single-qubit coherence and two-qubit entanglement are investigated in the Bloch channels with the indefinite causal order, which is created by means of a quantum switch. Coherence and entanglement are quantified respectively in terms of l ₁ -norm and negativity. It is shown that both coherence and entanglement with the indefinite causal order are larger than those without the indefinite causal order. In fact, the coherence remains finite even in the long-time limit. Contrary to expectations, it becomes larger as the environmental temperature increases. Furthermore, it is found that the entanglement becomes larger and survives longer than that in the absence of the indefinite causal order.