Nonasymptotic bounds for quantum purity amplification
Jack Spilecki | UC Berkeley
In quantum purity amplification, one is given n copies of a noisy quantum state ρ∈ℂd×d and asked to prepare k copies of its principal eigenstate |vd⟩. Several prior works have derived information-theoretically optimal algorithms for this problem, but the bounds they prove are only shown in the asymptotic regime as the number of samples n tends to infinity. In this paper, we establish the following nonasymptotic guarantee: if ρ's eigenvalues are sorted p1≤⋯≤pd and pd−1<pd, then n=O(k+kδ⋅1−pd(pd−pd−1)2) copies suffice to output a state with fidelity at least 1−δ with |v⊗kd⟩. Our bound holds for arbitrary spectra, and is independent of the dimension d. In the case of depolarizing noise, our finite-sample guarantee matches the optimal asymptotic scaling. Our proof is based on the combinatorics of random Young diagrams.
Location
- QNC 4104
- Online on Zoom
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Meeting ID: 912 8146 6256
Passcode
: 494237
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