Spacetime Path Integrals for Entangled States

Publication Date

2-1-2022

Document Type

Article

Publication Title

Foundations of Physics

Volume

52

Issue

1

DOI

10.1007/s10701-021-00520-2

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.

Keywords

Quantum entanglement, Schmidt basis, Sum over histories

Department

Physics and Astronomy

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