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We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
The reliable characterization of quantum states is a fundamental task in quantum information science. For this purpose, quantum state tomography provides a standard framework for reconstructing quantum states from measurement data, yet it…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
In this paper, we examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum state tomography. We find that, in some important circumstances, an elaborate…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^3 n^2 \log(1/\delta) / \epsilon^4)$ copies of the input…
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum…
We revisit the problem of mutually unbiased measurements in the context of estimating the unknown state of a $d$-level quantum system, first studied by W. K. Wootters and B. D. fields[7] in 1989 and later investigated by S. Bandyopadhyay et…
Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used…
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In…
We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine then sends an $O(\log(mn))$-length message to a server, at…
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 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…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where…