Causal confusion in quantum systems: distinguishing direct cause and common cause
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.
Related
- Elimination of quantum causal confusion in the presence of dual states
- Distinguishing Coherent Crosstalk from Calibration Drift via Pauli-Transfer Signatures and Quantum Edge Detection
- Distinguishing Quantum Capacitance Signatures of a Topological Majorana Wire from a Normal Wire Segment
- The Fock Space Dynamics of Causal Fermion Systems: Non-Abelian Gauge Fields
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BibTeX
@misc{tolotti2026causal,
title = {{Causal confusion in quantum systems: distinguishing direct cause and common cause}},
author = {Krisztina Tolotti and Riley Blank-Matthews and Arthur J. Parzygnat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10004},
eprint = {2610.10004},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10004},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causal confusion in quantum systems: distinguishing direct cause and common cause
AU - Krisztina Tolotti
AU - Riley Blank-Matthews
AU - Arthur J. Parzygnat
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10004
UR - https://arxiv.org/abs/2610.10004
AB - 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.
ER -