bibkey: song2024causalclassification
authors: Minjeong Song; Varun Narasimhachar; Bartosz Regula; Thomas J. Elliott; Mile Gu
year: 2024
title: "Causal Classification of Spatiotemporal Quantum Correlations"
doi: 10.1103/PhysRevLett.133.110202
url: https://arxiv.org/abs/2306.09336v2
claim: "The paper classifies two-qubit pseudo-density operators by their compatibility with spatial and temporal distribution mechanisms, characterizes temporal compatibility by R_AB = (id_A ⊗ Λ)K_AB for a quantum channel Λ, introduces an atemporality measure f, and asks whether atemporality is guaranteed by steering or Bell nonlocality."
strata_touched:
  - D5/S3/Quantum/Contextuality/SteeringTemporalCompatibilityRefutation
license: citation-only
triage: anchor

Causal Classification of Spatiotemporal Quantum Correlations

M. Song, V. Narasimhachar, B. Regula, T. J. Elliott and M. Gu, arXiv:2306.09336v2 (2024-09-23); Phys. Rev. Lett. 133, 110202 (2024). Quotations are from the v2 TeX source.

Spatial and temporal compatibility:

PDOs that lie outside of $\text{calS}$ are referred to as \emph{aspatial}, and those that lie outside of $\text{calT}$ are referred to as \emph{atemporal}.

The atemporality measure:

Consider first a \emph{forward atemporality} measure $\overrightarrow{f}$ that is zero if and only if ${\mathbf{R}}_{AB}$ has statistics consistent with a temporal distribution mechanism from $A$ to $B$; and a \emph{reverse atemporality} measure $\overleftarrow{f}$ that is zero if and only if ${\mathbf{R}}_{AB}$ has statistics consistent with a temporal distribution mechanism from $B$ to $A$.

Temporal PDOs (Eq. (3)):

\R_{AB} = \left(\id_A \ten \overrightarrow{\Lambda} \right) \K_{AB}

where ${\text{K}}_{AB}\equiv \left\{{\text{brho}}_A\text{ten}\frac{{\text{I}}_B}{2},{\S }_{AB}\right\}$ with ${\text{brho}}_A\equiv {\mathrm{tr}}_B{\mathbb{R}}_{AB}$ being the first marginal, $\{\cdot ,\cdot \}$ the anti-commutator, $\text{I}$ the identity operator, and $\S$ the swap operator.

The question:

Some entangled states are not atemporal, so is atemporality a strictly stronger notion of quantum correlations? And if so, is it guaranteed by steering or Bell non-locality~\cite{wiseman2007steering}?

Verified locator

• URL: https://arxiv.org/abs/2306.09336v2 (source main.tex, md5 c5fe67a443f5759537cc8ec3fdd2b1d5):
  • spatial and temporal compatibility, l. 356;
  • the atemporality measure, l. 377;
  • Eq. (3), l. 395–399;
  • the question, l. 469.
• DOI: https://doi.org/10.1103/PhysRevLett.133.110202.