Jack Spilecki

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quant-ph2026

Pretty good shadow tomography

Sabee Grewal, Angelos Pelecanos, Jack Spilecki +2

We give a shadow tomography algorithm that uses $O (lo g (m) lo g (m / δ) / ε^{2})$ copies of the input state. Specifically, given a quantum state $ρ$ and observables $O_1,\ldot…

quant-ph2026

Optimal cloning of mixed states

Marco Fanizza, Dmitry Grinko, Thilo Scharnhorst +1

We consider the problem of approximate cloning of quantum states: given $n$ copies of an unknown state $ρ \in C^{d \times d}$ , prepare an $(n + k)$ -copy state with high fidel…

quant-ph2026

The Keyl-Werner algorithm is not optimal for spectrum estimation

Angelos Pelecanos, Jack Spilecki, Ewin Tang +1

We give an algorithm which, given $n = O (d^{2} \cdot (lo g lo g (d) / lo g (d))^{2})$ copies of $ρ$ , estimates the eigenvalues of $ρ$ to constant error in total variation distance. Thus, we…

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 $ρ \in C^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\r…

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 $ρ \in C^{d \times d}$ and asked to produce an estimator of $ρ$ . In t…

quant-ph2025

Optimal lower bounds for quantum state tomography

Thilo Scharnhorst, Jack Spilecki, John Wright

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