Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states Article Swipe

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Physics Bipartite graph Rotation formalisms in three dimensions Unification Statistical physics Density matrix Quantum process Quantum state Quantum Matrix (chemical analysis) State (computer science) Process (computing) Theoretical physics Quantum mechanics Algorithm Theoretical computer science Quantum dynamics Mathematics Computer science Composite material Graph Geometry Programming language Materials science Operating system

Xiangjing Liu , Zhian Jia , Yixian Qiu , Fei Li , Oscar Dahlsten ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1088/1367-2630/ad264c · OA: W4391544450

We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have shown that bipartite two-time states can reproduce the statistics of bipartite process matrices. Here, we show that the operational scenarios underlying two-time states can be represented as PDMs, and thereby construct a mapping from process matrices with measurements to PDMs. The existence of this mapping implies that PDMs can, like the process matrix, model processes with indefinite causal orders. The results contribute to the unification of quantum models of spatiotemporal states.