Spacetime Path Integrals for Entangled States

TL;DR

This paper extends the path-integral formalism to all pure two-qubit states and some three-qubit states, enabling path-based calculations of entangled states in ordinary space and time, which could simplify quantum analysis.

Contribution

It demonstrates how to perform path-integral calculations for all pure two-qubit states and certain three-qubit states, broadening the applicability of the formalism.

Findings

Path integrals reproduce quantum correlations for two-qubit states.

Extension of path-integral methods to arbitrary measurement bases.

Simplification of quantum analysis through path-based calculations.

Abstract

Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of entangled states as entities in a high-dimensional Hilbert space, or the intuitive view of these states as a connection between distant spatial configurations, it may not even be obvious that a path-based calculation can be achieved using only paths in ordinary space and time. Previous work has shown how to do this for certain special states; this paper extends those results to all pure two-qubit states, where each qubit can be measured in an arbitrary basis. Certain three-qubit states are also developed, and path integrals again reproduce the usual correlations. These results should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective, simplifying certain calculations, and more generally informing research in quantum foundations.