Abstract
The field of indefinite causal order (ICO) has seen a recent surge in interest. Much of this research has focused on the quantum switch, wherein multiple parties act in a superposition of different orders in a manner transcending the quantum circuit model. This results in a new resource for quantum protocols, and is exciting for its relation to issues in foundational physics. The quantum switch is also an example of a higher-order quantum operation, in that it transforms not only quantum states but also other quantum operations. To date, no quantum process without a definite causal order has been completely experimentally characterized. Indeed, past work on the quantum switch has confirmed its ICO by measuring causal witnesses or demonstrating resource advantages, but the complete process matrix has been described only theoretically. Here we report our performing higher-order quantum process tomography. However, doing so requires exponentially many measurements with a scaling worse than that of standard process tomography. We overcome this challenge by creating a new passively stable fiber-based quantum switch using active optical elements to deterministically generate and manipulate time-bin encoded qubits. Moreover, our new architecture for the quantum switch can be readily scaled to multiple parties. By reconstructing the process matrix, we estimate its fidelity and tailor different causal witnesses directly for our experiment. To achieve this, we measure a set of tomographically complete settings, which also spans the input operation space. Our tomography protocol allows the characterization and debugging of higher-order quantum operations with and without an ICO, while our experimental time-bin techniques could enable the creation of a new realm of higher-order quantum operations with an ICO.
- Received 1 June 2023
- Accepted 22 December 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010325
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Within quantum mechanics, indefinite causal orders represent a fascinating phenomenon where quantum information travels between parties in a way that obscures the sequence of events. In such a process, it is genuinely impossible to determine which order the information is shared between the parties. These unique processes, which cannot be represented by conventional quantum circuits, promise to surpass standard quantum computers for specific tasks. However, conventional quantum tomography cannot describe these processes, and their experimental creation has demanded an impractical number of optical beams to traverse each party, posing significant scalability issues.
Our work addresses these hurdles by introducing a new technique to create the quantum switch, a process with an indefinite casual order. We route quantum information to different parties based on a photon’s temporal profile. Consequently, when the photon is in a superposition of different temporal modes, different causal orders are coherently superposed, while only a single beam passes through each party. Importantly, our method is readily scalable, paving the way for multiple-party applications.
In tandem with this development, we have introduced a “higher-order process tomography.” This allows us to treat different parties as inputs to the quantum switch. This allows for fully characterizing causally indefinite processes for the first time, providing new insight into these unique quantum processes.
By providing these powerful new tools, our work enriches the field of experimental studies of indefinite causal orders, driving forward our understanding and exploration of the compelling world of indefinite causal orders.
