Related papers: Optimal quantization for a probability measure on …
In the probabilistic construction of K\"ahler-Einstein metrics on a complex projective algebraic manifold X - involving random point processes on X - a key role is played by the partition function. In this work a new quantitative bound on…
We propose a new generalized remote state preparation protocol for using non-maximally entangled state as a shared resource. Different from the previous schemes, the parameters of measurement basis depend on not only the state of…
We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of…
A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a…
Given a compactly supported probability measure on a Riemannian manifold, we study the asymptotic speed at which it can be approximated (in Wasserstein distance of any exponent p) by finitely supported measure. This question has been…
We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success…
We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
According to a well-known theorem of Cram\'er and Wold, if $P$ and $Q$ are two Borel probability measures on $\mathbb{R}^d$ whose projections $P_L,Q_L$ onto each line $L$ in $\mathbb{R}^d$ satisfy $P_L=Q_L$, then $P=Q$. Our main result is…
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the EPR setting, we prove…
We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…