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Streaming quantum state purification for general mixed states
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Streaming quantum state purification for general mixed states
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Given multiple copies of a mixed quantum state with an unknown, nondegenerate principal eigenspace, quantum state purification is the task of recovering a quantum state that is closer to the principal eigenstate. A streaming protocol relying on recursive swap tests has been proposed and analysed for noisy depolarized states with arbitrary dimension and noise level. Here, we show that the same algorithm applies much more broadly, enabling the purification of arbitrary mixed states with a nondegenerate principal eigenvalue. We demonstrate this through two approaches. In the first approach, we show that, given the largest two eigenvalues, the depolarized noise is the most difficult noise to purify for the recursive swap tests, thus the desirable bounds on performance and cost follow from prior work. In the second approach, we provide a new and direct analysis for the performance of purification using recursive swap tests for the more general noise. We also derive simple lower bounds on the sample complexity, showing that the recursive swap test algorithm attains optimal sample complexity (up to a constant factor) in the low-noise regime.
Forward citations
Cited by 6 Pith papers
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Nonasymptotic bounds for quantum purity amplification
Derives dimension-independent nonasymptotic bounds for preparing k copies of the dominant eigenvector from noisy quantum states using random Young diagram combinatorics.
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An Exponential Sample-Complexity Advantage for Coherent Quantum Inference
Coherent quantum inference achieves O(1/ε) sample complexity for d-dimensional quantum purity amplification, exponentially better than the Ω(d/ε) required by any incoherent measurement-mediated protocol.
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Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
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Forward-Assisted Purification: A Spatiotemporal Framework Beyond Conventional Limits
Introduces forward-assisted purification via a new spatiotemporal framework that outperforms conventional static purification by up to 50x in copy efficiency and circumvents no-purification theorems for Bell states.
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Scaling-optimal purification of noisy qubit unitary channels
A U(2)-covariant parallel protocol based on a novel entanglement-assisted QECC purifies noisy qubit unitaries with O(1/n) noise scaling shown to be asymptotically optimal in the low-noise regime.
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Hybrid Quantum Error Correction and Mitigation by Purification
A SWAP-test purification protocol that estimates observables of ρ^N from noisy copies without postselection; the claimed mid-circuit quantum error correction is not established because no physical purified state is produced.
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