Related papers: Optimal error regions for quantum state estimation
One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…
Entanglement does not correspond to any observable and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more proper observables. Here we address…
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure…
In this paper we address the problem of using one probability space for estimating parameters and predicting future data when the observed data come from multiple contexts and thus from distinct spaces. We explain that a set-based…
We consider the problem of discriminating qubit states that are sent over a quantum channel and derive a necessary and sufficient condition for an optimal measurement to be preserved by the channel. We apply the result to the…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form ${\mathbf{z}\in\mathbb{R}^d:f(\mathbf{z})\leq\beta}$, where f is…
Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
When measuring phase of quantum states of light, the optimal single-shot measurement implements projection on the un-physical phase states. If we want to improve the precision further we need to accept a reduced probability of success,…
We derive general discrimination of quantum states chosen from a certain set, given initial $M$ copies of each state, and obtain the matrix inequality, which describe the bound between the maximum probability of correctly determining and…
This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
We study an optimized measurement which discriminates N mixed quantum states occurring with given prior robabilities. The measurement yields the maximum achievable confidence for each of the N conclusive outcomes, thereby keeping the…
Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the…
A minimal set of measurement operators for quantum state tomography has in the non-degenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here, we consider the situation where the…
We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.