Partial transpose as a space-time swap

TL;DR

This paper reveals that the partial transpose operation in quantum theory can be physically interpreted as swapping space and time, transforming spatial correlations into temporal ones, with implications for understanding entanglement and black hole physics.

Contribution

It provides a novel physical interpretation of partial transpose as a space-time swap, linking spatial and temporal correlations in bipartite quantum systems.

Findings

Partial transpose maps spatial correlations to temporal correlations.

For maximally entangled qubits, it converts Bell violations into causal correlations.

Suggests a connection between black hole horizons and quantum partial transposition.

Abstract

While the partial transpose operation appears in many fundamental results in quantum theory -- such as the Peres-Horodecki criterion for entanglement detection -- a physical interpretation of the partial transpose is lacking. In this work, we show that a partial transpose of a bipartite density operator is a two-time pseudo-density operator, which by definition encodes temporal correlations associated with two-point sequential measurement scenarios. As such, it follows that partial transposition admits a precise physical interpretation as mapping spatial correlations to temporal correlations, thus swapping the roles of space and time for bipartite quantum systems. For maximally entangled qubits, we show that partial transposition maps spatial correlations which violate Bell inequalities to causal correlations which cannot be replicated by spacelike separated systems, thus further solidifying the interpretation of partial transpose as a space-time swap. As it is known that gravitational effects swap the roles of space and time inside a black hole, our results suggest that at a quantum mechanical level, a traversal of a black hole's event horizon by a bipartite quantum system may be described by a partial transpose.