Quantum channel learning with limited parallel access
Abstract
Quantum channels can be characterized by their action on an orthogonal operator basis, where these operators are related to observable properties of the quantum system. For qudit and multimode bosonic systems, this is encoded respectively in the Heisenberg--Weyl transfer matrix estimated from the Choi-state, and in the characteristic-function transfer map estimated from a two-mode squeezed vacuum based Choi-state. We derive sample-complexity bounds for estimating entries of the transfer matrix/map to additive accuracy ε with success probability ≥1−δ, under different resources: access to the complex-conjugate channel ℰ* and/or parallel access to c copies. In all settings, the learner uses parallel channel calls with adaptively chosen, ancilla-assisted input states and measurements. Absolute values of transfer-matrix entries can be learned efficiently with simultaneous access to ℰ and ℰ*, with tight scaling ε−4. Without conjugate access, any c<d copies are insufficient for efficient learning, requiring sample complexity exponential in the number of (d-level) qudits n (for prime d). Efficiency is recovered at c=d, with tight scaling ε−2d. For bosonic systems, exponential sample complexity holds in terms of an effective dimension induced by an energy constraint for all c=O(1/ε). Although the task is learning a particular state, these bounds carry stronger implications than standard state-learning bounds since the learner controls the inputs and has ancillary assistance. This establishes a hierarchy of channel-learning resources: self-complex-conjugate channels require two-copy ancilla-assisted access for efficient learning, while for every square-free d, some channels require d-copy access. As a corollary, we derive tighter lower bounds for state learning with limited multi-copy access.
Related
- An exponential query advantage from access to Stinespring dilation unitaries in quantum channel learning
- Query-optimal unitary channel tomography in diamond distance with parallel access
- Parallel Quantum Advantage with Limited Adaptivity Requires Structure
- Parallel quantum channel discrimination and numerical ranges in tensor product subspaces
- Optimal Stabilizer Testing and Learning with Limited Quantum Memory
BibTeX
@misc{subramanian2026quantum,
title = {{Quantum channel learning with limited parallel access}},
author = {Mahadevan Subramanian and Hyukgun Kwon and Liang Jiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.05307},
eprint = {2608.05307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.05307},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum channel learning with limited parallel access
AU - Mahadevan Subramanian
AU - Hyukgun Kwon
AU - Liang Jiang
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2608.05307
UR - https://arxiv.org/abs/2608.05307
AB - Quantum channels can be characterized by their action on an orthogonal operator basis, where these operators are related to observable properties of the quantum system. For qudit and multimode bosonic systems, this is encoded respectively in the Heisenberg--Weyl transfer matrix estimated from the Choi-state, and in the characteristic-function transfer map estimated from a two-mode squeezed vacuum based Choi-state. We derive sample-complexity bounds for estimating entries of the transfer matrix/map to additive accuracy ε with success probability ≥1−δ, under different resources: access to the complex-conjugate channel ℰ^* and/or parallel access to c copies. In all settings, the learner uses parallel channel calls with adaptively chosen, ancilla-assisted input states and measurements. Absolute values of transfer-matrix entries can be learned efficiently with simultaneous access to ℰ and ℰ^*, with tight scaling ε^−4. Without conjugate access, any c<d copies are insufficient for efficient learning, requiring sample complexity exponential in the number of (d-level) qudits n (for prime d). Efficiency is recovered at c=d, with tight scaling ε^−2d. For bosonic systems, exponential sample complexity holds in terms of an effective dimension induced by an energy constraint for all c=O(1/ε). Although the task is learning a particular state, these bounds carry stronger implications than standard state-learning bounds since the learner controls the inputs and has ancillary assistance. This establishes a hierarchy of channel-learning resources: self-complex-conjugate channels require two-copy ancilla-assisted access for efficient learning, while for every square-free d, some channels require d-copy access. As a corollary, we derive tighter lower bounds for state learning with limited multi-copy access.
ER -