Streaming the partial-transpose moment hierarchy with order-independent quantum memory
Abstract
Partial transposition reveals mixed-state entanglement through the spectrum of ρABTB, but this operator is not generally a physical state. Its power moments are accessible through collective permutations, whose coherent width grows with moment order. Here we introduce a streaming protocol that processes fresh copies sequentially while retaining one copy and a reusable ancilla. By realizing opposite cyclic permutations on the two subsystems, each measurement record yields unbiased estimators of all moments p2,…,pK through successive outcome products. For an n-qubit state, the protocol uses 2n+1 active qubits independent of K and O(Klog K/εmom2) copies, matching Ω(K/εmom2) lower bounds up to a logarithmic factor, including a PT-specific isospectral construction. Higher-order moments strengthen thermal-state entanglement certification toward the exact PPT threshold. Simulations cover pure and mixed states, and a cloud quantum processor implements a three-qubit instance.
Related
- Two-copy distillability of one-copy-undistillable negative-partial-transpose states in every dimension
- Online Estimation of Partial Transpose Moments via Fast Classical Updates
- Many-body entanglement quantification in arbitrary states through a few partial-transpose moments
- Spectral bounds for the partial transpose
- TandemQEC: Joint Provisioning of Streaming Quantum Error Correction in Tightly-Integrated Quantum-Classical Systems
BibTeX
@misc{huang2026streaming,
title = {{Streaming the partial-transpose moment hierarchy with order-independent quantum memory}},
author = {Junxiang Huang and Xiaoyang Wang and Xiao Yuan and Yukun Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.14204},
eprint = {2606.14204},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.14204},
}
RIS
TY - UNPB
TI - Streaming the partial-transpose moment hierarchy with order-independent quantum memory
AU - Junxiang Huang
AU - Xiaoyang Wang
AU - Xiao Yuan
AU - Yukun Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.14204
UR - https://arxiv.org/abs/2606.14204
AB - Partial transposition reveals mixed-state entanglement through the spectrum of ρ_AB^T_B, but this operator is not generally a physical state. Its power moments are accessible through collective permutations, whose coherent width grows with moment order. Here we introduce a streaming protocol that processes fresh copies sequentially while retaining one copy and a reusable ancilla. By realizing opposite cyclic permutations on the two subsystems, each measurement record yields unbiased estimators of all moments p_2,…,p_K through successive outcome products. For an n-qubit state, the protocol uses 2n+1 active qubits independent of K and O(Klog K/ε_mom^2) copies, matching Ω(K/ε_mom^2) lower bounds up to a logarithmic factor, including a PT-specific isospectral construction. Higher-order moments strengthen thermal-state entanglement certification toward the exact PPT threshold. Simulations cover pure and mixed states, and a cloud quantum processor implements a three-qubit instance.
ER -