Related papers: A note on the quantization error for in-homogeneou…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
This pedagogical article solves an interesting problem in quantum measure theory. Although a quantum measure $\mu$ is a generalization of an ordinary probability measure, $\mu$ need not satisfy the usual additivity condition. Instead, $\mu$…
We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of…
We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is…
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition--------quantum coherence or quantum superposition. In this paper, we attempt to give an alternative…
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of a quantum state under consideration. In…
We prove the following theorem. Let $\mu$ be a measure on $R^n$ with even continuous density, and let $K,L$ be origin-symmetric convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any central hyperplane H. Then $\mu(K)\le…
The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity…
Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
In this paper, we establish sufficient conditions for the existence of error bounds at infinity for lower semicontinuous inequality systems. We also show that the existence of an error bound at infinity of constraint systems plays an…
Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
The quantification of quantum coherence has attracted a growing attention, and based on various physical contexts, several coherence measures have been put forward. An interesting question is whether these coherence measures give the same…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…