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Classical Shadow Tomography with Locally Scrambled Quantum Dynamics · Around

2021

Classical Shadow Tomography with Locally Scrambled Quantum Dynamics

Hu, Hong-Ye, Choi, Soonwon, You, Yi-Zhuang

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We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis transformations.

In this case, the reconstruction map for the classical shadow tomography depends only on the average entanglement feature of classical snapshots.
We provide an unbiased estimator of the quantum state as a linear combination of reduced classical snapshots in all subsystems, where the combination coefficients are solely determined by the entanglement feature.
We also bound the number of experimental measurements required for the tomography scheme, so-called sample complexity, by formulating the operator shadow norm in the entanglement feature formalism.

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