Related papers: Collective vs local measurements in qubit mixed st…

We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement…

It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…

We demonstrate a method for super-resolving signals encoded as finite mixtures of bosonic modes using collective measurements that exploit permutation symmetry. Specifically, we use multiple copies of the state $\rho$ of the finite mixture…

We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this…

We initiate the study of sample-optimal quantum state tomography with minimal disturbance to the samples. Can we efficiently learn a precise description of a quantum state through sequential measurements of samples while at the same time…

We present a framework that formulates the quest for the most efficient quantum state tomography scheme as an optimization problem which can be solved numerically. This approach can be applied to a broad spectrum of relevant setups…

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here…

An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of…

Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the…

The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find…

We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to…

We consider the statistical problem of `compressive' estimation of low rank states with random basis measurements, where the estimation error is expressed terms of two metrics - the Frobenius norm and quantum infidelity. It is known that…

In this article, by treating minimum error state discrimination as a complementarity problem, we obtain the geometric optimality conditions. These can be used as the necessary and sufficient conditions to determine whether every optimal…

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden…

We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly non-orthogonal mixed quantum states. We show that if the quantum state ensemble…

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…

A quantum copying machine producing two (in general non-identical) copies of an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied using a quality measure based on distinguishability of states, rather than fidelity.…

We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this…

A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as…

Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…