Related papers: Random density matrices: Analytical results for me…
The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears…
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…
We develop a systematic method to calculate the trace distance between two reduced density matrices in 1+1 dimensional quantum field theories. The approach exploits the path integral representation of the reduced density matrices and an ad…
The average subsystem trace distance has been proposed as an indicator of quantum many-body chaos and integrability. In integrable systems, evaluating the trace distance faces two challenges: the computational cost for large systems and…
Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…
Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear…
This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…
A geometric interpretation for the A-fidelity between two states of a qubit system is presented, which leads to an upper bound of the Bures fidelity. The metrics defined based on the A-fidelity are studied by numerical method. An…
The aim of this paper is to provide a method for explicit computation of the Bures metric over the space of $N$-level quantum system, based on the coset parametrization of density matrices.
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling $t$ copies of a $d$-dimensional quantum state according to the Haar measure on the…
We address the problem of evaluating the difference between quantum states before and after being affected by errors encoded in unitary transformations. Standard distance functions, e.g., the Bures length, are not fully adequate for such a…
We evaluate a Gaussian entanglement measure for a symmetric two-mode Gaussian state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable Gaussian states. The required minimization procedure was…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
We compute the Bures distance between two thermal squeezed states and deduce the Statistical Distance metric. By computing the curvature of this metric we can identify regions of parameter space most sensitive to changes in these parameters…
The aim of the present note is to show that the method of our paper ArXiv:2408.11400 with minor extra efforts can be extended to obtain upper bounds for the Bures distance between quantum Gaussian states. We argue that these bounds are…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this…
Fidelity estimation for entangled states constitutes an essential building block for quality control and error detection in quantum networks. Nonetheless, quantum networks often encounter heterogeneous and correlated noise, leading to…
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…