Spacetime Path Integrals for Entangled States

• URL: http://arxiv.org/abs/2103.02425v2
• Date: Tue, 4 May 2021 20:12:16 GMT
• Title: Spacetime Path Integrals for Entangled States
• Authors: Narayani Tyagi and Ken Wharton
• Abstract summary: This paper shows how to implement path-based calculations for multi-qubit entangled states. It should allow for a substantial amount of conventional quantum analysis to be translated over into a path-integral perspective.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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