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This research establishes a rigorous operational definition for Positive-Partial-Transpose (PPT) channels by linking them to "causal confusion," where sequential and parallel measurement protocols yield identical joint expectation values. The study further characterizes entanglement-breaking channels as the specific set of qubit channels capable of inducing this ambiguity, providing new theoretical tools for quantum information processing.
Causal confusion in quantum systems: distinguishing direct cause and common cause
arXiv:2610.10004v1 Announce Type: new Abstract: The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.
Abstract:The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.
32 pages, 17 figures; comments welcome!
arXiv:2610.10004 [quant-ph]
(or arXiv:2610.10004v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.10004 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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