Relativity of spacetime ontology: When correlations in space become correlata in time

TL;DR

This paper explores how quantum correlations and correlata are not inherently distinct but depend on the tensor product structure, leading to the possibility that spatial correlations can manifest as temporal correlata and vice versa.

Contribution

It demonstrates that correlations and correlata are dual concepts dependent on tensor product decompositions, challenging traditional views and implications for quantum measurement theory.

Findings

Spatial correlations can become temporal correlata under different tensor structures.

Invariant 2-qubit states can be entangled or unentangled depending on the tensor product.

Implications for the uniqueness theorem of the singlet state and measurement theory.

Abstract

Challenging Mermin's perspective that ``correlations have physical reality; that which they correlate does not'' we argue that correlations and correlata are not fundamentally distinct. These are dual concepts depending on the tensor product decomposition defining subsystems. Since the same quantum states may be either entangled or separable, but with respect to alternative tensor product structures, a spatial correlation in one context can become a temporal correlatum in another, and vice versa. In consequence, 2-qubit states invariant under $V\otimes V$ can be either entangled or unentangled, in conflict with the well known uniqueness theorem about the singlet state, a fact with possible implications for the quantum measurement theory.