Jack Spilecki

works on

algorithmic sample complexity 1 eigenvalue estimation 1 principal component analysis 1 quantum state tomography 1 spectrum estimation 1

From the 1 of 5 linked papers with an AI index.

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quant-ph2026

The Keyl-Werner algorithm is not optimal for spectrum estimation

Angelos Pelecanos, Jack Spilecki, Ewin Tang +1

The paper presents a new algorithm that estimates the eigenvalues of a quantum state using fewer copies than the traditional Keyl‑Werner method, achieving constant error with O(d^2…

quant-ph2026

Nonasymptotic bounds for quantum purity amplification

Thilo Scharnhorst, Jack Spilecki, John Wright

In quantum purity amplification, one is given $n$ copies of a noisy quantum state $I ¨ \in C^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\…

quant-ph2025

Mixed state tomography reduces to pure state tomography

Angelos Pelecanos, Jack Spilecki, Ewin Tang +1

A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state alg…

quant-ph2025

The debiased Keyl's algorithm: a new unbiased estimator for full state tomography

Angelos Pelecanos, Jack Spilecki, John Wright

In the problem of quantum state tomography, one is given $n$ copies of an unknown rank- $r$ mixed state $I ¨ \in C^{d \times d}$ and asked to produce an estimator of $I ¨ $ . In…

quant-ph2025

Optimal lower bounds for quantum state tomography

Thilo Scharnhorst, Jack Spilecki, John Wright

We show that $n = I^c ◯ (r d / ε^{2})$ copies are necessary to learn a rank $r$ mixed state $I ¨ \in C^{d \times d}$ up to error $ε$ in trace distance. This match…