Spacetime Path Integrals for Entangled States
Foundations of Physics
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.
Quantum entanglement, Schmidt basis, Sum over histories
Physics and Astronomy
Narayani Tyagi and Ken Wharton. "Spacetime Path Integrals for Entangled States" Foundations of Physics (2022). https://doi.org/10.1007/s10701-021-00520-2