Related papers: Improved classical shadows from local symmetries i…
We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total…
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Classical shadow tomography serves as a potent tool for extracting numerous properties from quantum many-body systems with minimal measurements. Nevertheless, prevailing methods yielding optimal performance for few-body operators…
We show that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 - \epsilon$ fidelity. This improves upon the tomography lower bounds…
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum…
In this article we develop a continuous variable (CV) shadow tomography scheme with wide ranging applications in quantum optics. Our work is motivated by the increasing experimental and technological relevance of CV systems in quantum…
We introduce a post-processing technique for classical shadow measurement data that enhances the precision of ground state estimation through high-dimensional subspace expansion; the dimensionality is only limited by the amount of classical…
"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random…
Accurately estimating the properties of quantum systems is a central challenge in quantum computing and quantum information. We propose a method to obtain unbiased estimators of multiple observables with low statistical error by…
We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\rho$, estimate $\text{tr}(P\rho)$ for some set of Pauli operators $P$ to within additive error $\epsilon$. This has been a popular…
In the quantum state tomography problem, one wishes to estimate an unknown $d$-dimensional mixed quantum state $\rho$, given few copies. We show that $O(d/\epsilon)$ copies suffice to obtain an estimate $\hat{\rho}$ that satisfies…
Shadow tomography is a scalable technique to characterise the quantum state of a quantum computer or quantum simulator. The protocol is based on the transformation of the outcomes of random measurements into the so-called classical shadows,…
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A…
How many copies of a mixed state $\rho \in \mathbb{C}^{d \times d}$ are needed to learn its spectrum? To date, the best known algorithms for spectrum estimation require as many copies as full state tomography, suggesting the possibility…
We provide a new perspective on shadow tomography by demonstrating its deep connections with the general theory of measurement frames. By showing that the formalism of measurement frames offers a natural framework for shadow tomography --…
Expectation values of observables are routinely estimated using so-called classical shadows$\unicode{x2014}$the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow…
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…