Related papers: Learning Distributions over Quantum Measurement Ou…
We study quantum state testing where the goal is to test whether $\rho=\rho_0\in\mathbb{C}^{d\times d}$ or $\|\rho-\rho_0\|_1>\varepsilon$, given $n$ copies of $\rho$ and a known state description $\rho_0$. In practice, not all measurements…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
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…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
Reconstructing the state of a complex quantum system represents a pivotal task for all quantum information applications, both for characterization purposes and for verification of quantum protocols. Recent technological developments have…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
Following [OW16], we continue our analysis of: (1) "Quantum tomography", i.e., learning a quantum state, i.e., the quantum generalization of learning a discrete probability distribution; (2) The distribution of Young diagrams output by the…
This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically,…
Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key…
Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of…
Characterization of quantum systems from experimental data is a central problem in quantum science and technology. But which measurements should be used to gather data in the first place? While optimal measurement choices can be worked out…
Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have…