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

Xiangjing Liu; Zhian Jia; Yixian Qiu; Fei Li; Oscar Dahlsten

doi:10.1088/1367-2630/ad264c

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

Xiangjing Liu^*
, Zhian Jia^*
, Yixian Qiu
, Fei Li
, Oscar Dahlsten^*

^*Corresponding author for this work

Department of Physics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

11 Citations (Scopus)

46 Downloads (CityUHK Scholars)

Abstract

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. © 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

Original language	English
Article number	033008
Journal	New Journal of Physics
Volume	26
Issue number	3
Online published	13 Mar 2024
DOIs	https://doi.org/10.1088/1367-2630/ad264c
Publication status	Published - Mar 2024

Funding

X L, F L and O D acknowledge support from the National Natural Science Foundation of China (Grants Nos. 12050410246, 1200509 and 12050410245) and City University of Hong Kong (Project No. 9610 623). Y Q is supported by the National Research Foundation, Singapore and A∗ STAR under its CQT Bridging Grant. Z J is supported by the National Research Foundation and the Ministry of Education in Singapore through the Tier 3 MOE2012-T3-1-009 Grant for Random numbers from quantum processes.

Research Keywords

indefinite causality
multiple-time states
process matrix
pseudo-density matrix
spacetime states

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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abstract = "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. {\textcopyright} 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.",

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author = "Xiangjing Liu and Zhian Jia and Yixian Qiu and Fei Li and Oscar Dahlsten",

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T1 - Unification of spatiotemporal quantum formalisms

T2 - mapping between process and pseudo-density matrices via multiple-time states

AU - Liu, Xiangjing

AU - Jia, Zhian

AU - Qiu, Yixian

AU - Li, Fei

AU - Dahlsten, Oscar

PY - 2024/3

Y1 - 2024/3

N2 - 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. © 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

AB - 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. © 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

KW - indefinite causality

KW - multiple-time states

KW - process matrix

KW - pseudo-density matrix

KW - spacetime states

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U2 - 10.1088/1367-2630/ad264c

DO - 10.1088/1367-2630/ad264c

M3 - RGC 21 - Publication in refereed journal

SN - 1367-2630

VL - 26

JO - New Journal of Physics

JF - New Journal of Physics

IS - 3

M1 - 033008

ER -

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

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