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Related papers: Optimal tradeoffs for estimating Pauli observables

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Cross-platform verification is the task of comparing the output states produced by different physical platforms using solely local quantum operations and classical communication. While protocols have previously been suggested for this task,…

Quantum Physics · Physics 2025-09-22 Marcel Hinsche , Marios Ioannou , Sofiene Jerbi , Lorenzo Leone , Jens Eisert , Jose Carrasco

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure…

Quantum Physics · Physics 2021-07-21 Hsin-Yuan Huang , Richard Kueng , John Preskill

In this paper, we show that $\Theta(\mathrm{poly}(n)\cdot\frac{4^n}{\epsilon^2})$ is the sample complexity of testing whether two $n$-qubit quantum states $\rho$ and $\sigma$ are identical or $\epsilon$-far in trace distance using…

Quantum Physics · Physics 2020-09-25 Nengkun Yu

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the…

Quantum Physics · Physics 2019-07-19 Andrew Jena , Scott Genin , Michele Mosca

Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime:…

Quantum Physics · Physics 2026-04-30 Alireza Goldar , Zhen Qin , Zhihui Zhu , Zhe-Xuan Gong , Michael B. Wakin

The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum…

Quantum Physics · Physics 2023-07-07 Cambyse Rouzé , Daniel Stilck França

This paper presents tight upper and lower bounds for minimum number of samples (copies of a quantum state) required to attain a prescribed accuracy (measured by error variance) for scalar parameters estimation using unbiased estimators…

Quantum Physics · Physics 2025-05-20 Farhad Farokhi

We consider the classic question of state tomography: given copies of an unknown quantum state $\rho\in\mathbb{C}^{d\times d}$, output $\widehat{\rho}$ which is close to $\rho$ in some sense, e.g. trace distance or fidelity. When one is…

Quantum Physics · Physics 2023-05-31 Sitan Chen , Brice Huang , Jerry Li , Allen Liu , Mark Sellke

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…

Quantum Physics · Physics 2022-09-08 Weiyuan Gong , Scott Aaronson

Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…

Quantum Physics · Physics 2026-05-25 Yanglin Hu , Enrique Cervero-Martín , Elias Theil , Laura Mančinska , Marco Tomamichel

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows…

Quantum Physics · Physics 2015-06-26 E. Bagan , M. A. Ballester , R. Munoz-Tapia , O. Romero-Isart

We describe a new shadow tomography algorithm that uses $n=\Theta(\sqrt{m}\log m/\epsilon^2)$ samples, for $m$ measurements and additive error $\epsilon$, which is independent of the dimension of the quantum state being learned. This stands…

Quantum Physics · Physics 2024-11-05 Pulkit Sinha

We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state $\rho$ in order to learn a classical description which suffices to…

Quantum Physics · Physics 2024-06-19 Daniel Grier , Hakop Pashayan , Luke Schaeffer

We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors…

Quantum Physics · Physics 2014-12-23 Adam Miranowicz , Karol Bartkiewicz , Jan Perina , Masato Koashi , Nobuyuki Imoto , Franco Nori

Interfacing quantum and classical processors is an important subroutine in full-stack quantum algorithms. The so-called "classical shadow" method efficiently extracts essential classical information from quantum states, enabling the…

Quantum Physics · Physics 2025-09-11 Shuowei Ma , Junyu Liu

When sensitive information is encoded in data, it is important to ensure the privacy of information when attempting to learn useful information from the data. There is a natural tradeoff whereby increasing privacy requirements may decrease…

Quantum Physics · Physics 2026-02-12 Theshani Nuradha , Sujeet Bhalerao , Felix Leditzky

Pauli channels are ubiquitous in quantum information, both as a dominant noise source in many computing architectures and as a practical model for analyzing error correction and fault tolerance. Here we prove several results on efficiently…

Quantum Physics · Physics 2022-02-23 Steven T. Flammia , Joel J. Wallman

Given many copies of an unknown quantum state $\rho$, we consider the task of learning a classical description of its principal eigenstate. Namely, assuming that $\rho$ has an eigenstate $|\phi\rangle$ with (unknown) eigenvalue $\lambda >…

Quantum Physics · Physics 2024-07-09 Daniel Grier , Hakop Pashayan , Luke Schaeffer

Trace distance and infidelity (induced by square root fidelity), as basic measures of the closeness of quantum states, are commonly used in quantum state discrimination, certification, and tomography. However, the sample complexity for…

Quantum Physics · Physics 2024-10-29 Qisheng Wang , Zhicheng Zhang

Quantum shadow tomography based on the classical shadow representation provides an efficient way to estimate properties of an unknown quantum state without performing a full quantum state tomography. In scenarios where estimating the…

Quantum Physics · Physics 2026-03-13 Aniket Sengupta , Arijit Chatterjee , G. J. Sreejith , T. S. Mahesh