Indefinite causal order aids quantum depolarizing channel identification

Yongxi Yuan

Juan Gu, Zhimin Yin, Longsuo Li

Masashi Ban

Michael R. Frey

Indefinite causal ordering (ICO) refers to quantum channels arranged so that the path through them is a super- position of different possible paths. The ICO is called pure when the path superposition is a pure quantum state. Channel probing, in which probes in prepared quantum states are passed through copies of the channel to estimate one or more channel parameters, is aided by ICO. Specifically, pure ICO is known to increase the quantum Fisher information (QFI) in the processed probe state about the unknown parameter(s). We consider the case complementary to pure ICO in which the path state is maximally mixed for a given indefiniteness. Deriving the QFI under this condition by a new approach, we find that mixed ICO-assisted probing, while not as beneficial as pure ICO probing, still yields greater QFI than does the comparable scheme with definite causal order. The d-dimensional quantum depolarizing channel is used as the channel model for this study. While mixed ICO-assisted probing, like pure ICO-assisted probing, is generally advantageous for probing the depolarizing channel, mixed ICO's relative effectiveness decreases with probe dimension, just as for pure ICO-assisted probing, each being most effective for qubit probes.

Yaxin Wang, Linxiang Zhou, Tianfeng Feng +6 more

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.

Lorenzo M. Procopio, Francisco Delgado, Marco Enríquez +2 more

It has recently been shown that if two completely depolarizing channels are in a superposition of different orders, classical information can be transmitted that would be otherwise lost [1]. Here, we present a generalization of the results of [1] to study communication with arbitrary depolarizing channels and putting to good use indefinite causal order, a new paradigm for quantum information/computation.