Experimental demonstration of genuine quantum information transmission through completely depolarizing channels in a superposition of cyclic orders

Abstract

A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite causal order provides a promising solution by allowing control over the sequence in which channels are applied. We experimentally demonstrate the activation of quantum communication through completely depolarizing channels using a programmable silicon photonic quantum chip. By implementing configurations based on the superposition of cyclic orders, a form of indefinite causal order, we report the first experimental realization of genuine quantum information transmission across multiple concatenated completely depolarizing channels. Our results show that when four completely depolarizing channels are combined using the superposition of cyclic orders, the fidelity of the output state is $0.712 \pm 0.013$, significantly exceeding the classical threshold of 2/3. Our work establishes indefinite causal order as a powerful tool for overcoming noise-induced limitations in quantum communication, demonstrating its potential in high-noise environments and opening new possibilities for building robust quantum networks.

Figures (3)

• Figure 1: The schematic of a quantum state passing through four channels. (a) The quantum state passes sequentially through the channels $A$, $B$, $C$, and $D$ in a fixed order. (b) The quantum state passes through the channels $A$, $B$, $C$, and $D$ in a superposition of four different sequences.
• Figure 2: Schematic of the silicon quantum photonic chip and the external setup. The chip comprises five functional regions. (i) generation of single photons. (ii) preparation of the control state $|+\rangle$. (iii) preparation of the input state $\rho$. (iv) the input state $\rho$ passes through four completely depolarizing channels with indefinite causal order. Each channel is configured with equal probability to implement one of the Pauli operations $I$, $X$, $Y$, or $Z$, resulting in 256 different combinations, ranging from $IIII$, $IIIX$, to $ZZZZ$. For each input state $\rho$, these 256 configurations are applied, and the corresponding output data is accumulated, effectively simulating the passage of the quantum state through four completely depolarizing channels. (v) The output state $\rho^{\prime}$ is measured by projecting it onto the six quantum states $0$, $1$, $D$, $A$, $R$, $L$, with each projection being measured for 1 second. The total measurement time for each output state is $1 \times 256 \times 6 = 1536$ seconds. The two-photon coincidence count rate is 116.8/s. VOA, variable optical attenuation; FPC, fiber polarization controller; FA, fiber array; SNSPD, superconducting nanowire single-photon detector; CC, coincidence counting module.
• Figure 3: Experimental results of quantum state fidelity after propagation through multiple completely depolarizing channels under indefinite causal order. Four quantum states, $|D\rangle$, $|A\rangle$, $|R\rangle$, and $|L\rangle$, pass through $N=1,2,3,4$ completely depolarizing channels. When $N=4$, the average fidelity of the output states reaches $0.712 \pm 0.013$, surpassing the classical threshold of $2/3$.