A de Finetti theorem for quantum causal structures

• URL: http://arxiv.org/abs/2403.10316v2
• Date: Wed, 24 Apr 2024 12:20:01 GMT
• Title: A de Finetti theorem for quantum causal structures
• Authors: Fabio Costa, Jonathan Barrett, Sally Shrapnel,
• Abstract summary: Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems" 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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