A simple proof of unitary parallelization via port-based teleportation

Abstract:Port-based teleportation (PBT) is a variant of quantum teleportation that does not require corrections on the teleported state: starting with $N$ shared EPR states, Alice can teleport a qudit to Bob by performing a measurement on her system and informing Bob which of his $N$ `ports' to retrieve the state, up to infidelity decaying with $N$. Existing quantum circuits of PBT rely on representation theory tools and the mixed Schur transform. In this note, we report an elementary efficient circuit for PBT, which has depth $\operatorname{polylog}(N,d)$. As a corollary, this gives a simple proof that all $n$-qubit unitaries can be parallelized to $\operatorname{poly}(n)$ depth, recovering a recent result due to Nehoran--Slote--Yuen and OpenAI.

arXiv:2610.30761 [quant-ph]

(or arXiv:2610.30761v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.30761 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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