A de Finetti theorem for quantum causal structures

Journal article

What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems", which connect a simple and easy-to-justify condition – symmetry under exchange – with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest

Authors: Costa, F; Barrett, J; Shrapnel, S

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
• Journal: Quantum: the open journal for quantum science
• Volume: 9
• Pages: 1628-1628
• Article number: ARTN 1628
• Publication date: 2025-02-11
• DOI: 10.22331/q-2025-02-11-1628
• EISSN: 2521-327X
• ISSN: 2521-327X
• Language: English
• Keywords: Mathematical economics; Mathematics; Quantum; Statistical physics; Physics; Quantum mechanics