Self-testing Quantum Supermaps

• URL: http://arxiv.org/abs/2606.25124v1
• Date: Tue, 23 Jun 2026 19:54:13 GMT
• Title: Self-testing Quantum Supermaps
• Abstract summary: We show that quantum supermaps can be identified device-independently.<n>First self-test of both a quantum algorithmic comb and a causally indefinite quantum process.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: By certifying quantum operations from measurement statistics directly, without any assumption on the internal workings of the devices involved, self-testing enables a uniquely reliable identification of quantum objects. While such device-independent characterization has been shown to be possible for states, measurements and channels, it has so far not been extended to quantum supermaps -- operations that act on quantum channels themselves and can combine them in either a well-defined causal order or also, remarkably, in an indefinite causal order. Here we show that quantum supermaps can be identified device-independently. Specifically, we obtain two levels of certification, depending on the network structure of the experiment: when each slot of the supermap accepts a single uncharacterized black box, identification up to local embedding combs is obtained; when several black boxes are inserted within each slot, identification up to local extracting and injecting maps is achieved. We illustrate our approach on four examples -- the identity comb, a bit-flip error-correcting comb, the comb describing Grover's algorithm, and the quantum switch -- providing in particular the first self-test of both a quantum algorithmic comb and a causally indefinite quantum process. Notably, in the latter case, this provides a new way to certify causal indefiniteness in a device-independent manner.

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