One-to-One Correspondence Between Deterministic Port-Based Teleportation and Unitary Estimation
Abstract
Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations.We show that the optimal fidelity of deterministic port-based teleportation (dPBT) usingN=n+ 1 ports to teleport ad-dimensional state is equivalent to the optimal fidelity ofd-dimensional unitary estimation using n calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by 1 −O(d4)N−2≤F≤ 1−Ω(d4)N−2, which improves the previously known result given by 1 −O(d5)N−2≤ F ≤ 1 − Ω(d2)N−2. We also show that the optimal fidelity of unitary estimation for the case n ≤ d − 1 isF= n+1/d2, and this fidelity is equal to the optimal fidelity of unitary inversion withn≤d− 1 calls of the input unitary operation even if we allow indefinite causal order among the calls.
Related
- A simple proof of unitary parallelization via port-based teleportation
- Quantifying Teleportation Overhead in Distributed Unitary Coupled-Cluster Ansätze
- 2 + 2 = 4 a 2d/2d unitary/non-unitary correspondence
- Enabling chemically accurate quantum phase estimation in the early fault-tolerant regime via unitary weight concentration
- Optimal Diamond Distance Estimation for Unitary Channels
BibTeX
@article{yoshida2026onetoone,
title = {{One-to-One Correspondence Between Deterministic Port-Based Teleportation and Unitary Estimation}},
author = {Satoshi Yoshida and Yuki Koizumi and Michał Studziński and Marco Túlio Quintino and Mio Murao},
journal = {IEEE Transactions on Information Theory},
year = {2026},
month = oct,
doi = {10.1109/tit.2026.3658543},
eprint = {2408.11902},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05787655v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - One-to-One Correspondence Between Deterministic Port-Based Teleportation and Unitary Estimation
AU - Satoshi Yoshida
AU - Yuki Koizumi
AU - Michał Studziński
AU - Marco Túlio Quintino
AU - Mio Murao
PY - 2026
DA - 2026/10/08
JO - IEEE Transactions on Information Theory
DO - 10.1109/tit.2026.3658543
UR - https://hal.science/hal-05787655v1
AB - Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations.We show that the optimal fidelity of deterministic port-based teleportation (dPBT) usingN=n+ 1 ports to teleport ad-dimensional state is equivalent to the optimal fidelity ofd-dimensional unitary estimation using n calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by 1 −O(d4)N−2≤F≤ 1−Ω(d4)N−2, which improves the previously known result given by 1 −O(d5)N−2≤ F ≤ 1 − Ω(d2)N−2. We also show that the optimal fidelity of unitary estimation for the case n ≤ d − 1 isF= n+1/d2, and this fidelity is equal to the optimal fidelity of unitary inversion withn≤d− 1 calls of the input unitary operation even if we allow indefinite causal order among the calls.
SN - 0018-9448
ER -