Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data
Abstract
Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically complete, so the underlying process cannot in general be reconstructed exactly from the observed distribution. As a result, causal direction can be statistically identifiable in some cases but fundamentally indistinguishable in others. In this work, we determine necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction. We show that directional conditional-independence structure and the positivity criterion based on the pseudo-density matrix, as developed in recent work by We show that directional conditional-independence structure and PDM-based positivity criteria are not sufficient by themselves. We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable. In this regime, we characterize when the two sequential directions are statistically indistinguishable, and we show by example that positivity alone does not exclude more general memoryful strategies, whereas the additional algebraic consistency requirement does.
Related
- Sequential Capacity of Quantum Processes with Finite Memory
- Developing Multi-Dimensional, Sequential sWeighting Routines for Reaction Selection with Emphasis on Kaon Identification at CLAS12
- Polarisation-resolved identification of spontaneous four-wave mixing processes in a multimode fused tapered fibre coupler
- Conditions for implementing projective measurements through continuous monitoring
- A Restricted Boltzmann Machine with Quantum-State Visible Units
BibTeX
@misc{hayashi2026causalorder,
title = {{Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data}},
author = {Masahito Hayashi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04571},
eprint = {2605.04571},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04571},
}
RIS
TY - UNPB
TI - Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data
AU - Masahito Hayashi
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2605.04571
UR - https://arxiv.org/abs/2605.04571
AB - Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically complete, so the underlying process cannot in general be reconstructed exactly from the observed distribution. As a result, causal direction can be statistically identifiable in some cases but fundamentally indistinguishable in others. In this work, we determine necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction. We show that directional conditional-independence structure and the positivity criterion based on the pseudo-density matrix, as developed in recent work by We show that directional conditional-independence structure and PDM-based positivity criteria are not sufficient by themselves. We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable. In this regime, we characterize when the two sequential directions are statistically indistinguishable, and we show by example that positivity alone does not exclude more general memoryful strategies, whereas the additional algebraic consistency requirement does.
ER -