Enhanced Communication with the Assistance of Indefinite Causal Order

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter, we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, noncommuting processes, whose order (or lack thereof) can affect the ability to transmit information.

Figure 1

Fixed order vs superposition of orders. 1(a) A quantum particle, prepared in the state $\rho$, goes first through channel ${\mathcal{N}}_1$ and then through channel ${\mathcal{N}}_2$. This configuration is associated to the state ${\rho }_c=|1⟩⟨1|$ of a control qubit, in which the choice of order is encoded. 1(b) The quantum particle goes first through ${\mathcal{N}}_2$ and then through ${\mathcal{N}}_1$. This alternative configuration is associated to the qubit state ${\rho }_c=|0⟩⟨0|$. 1(c) The quantum switch creates a superposition of the two configurations 1(a) and 1(b). It takes a control qubit in a superposition state, such as ${\rho }_c=|+⟩⟨+|$, and correlates the order of the two channels with the state of the qubit.