Related papers: Distances between pure quantum states induced by a…
Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical…
We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
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…
It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of…
We present a construction of Hermitian operators and quantum states labelled by strings from a finite field. The distance between these operators or states is then simply related (typically, proportional) to the Hamming distance between…
Quasi-states are certain not necessarily linear functionals on the space of continuous functions on a compact Hausdorff space. They were discovered as a part of an attempt to understand the axioms of quantum mechanics due to von Neumann. A…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…
The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to…
The information metric provides a unique notion of distance along any continuous family of physical theories, placing two theories further apart the more distinguishable they are. As such, the information metric is typically singular at…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the…
We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the…
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally…
The distance-minimizing data-driven computational mechanics has great potential in engineering applications by eliminating material modeling error and uncertainty. In this computational framework, the solution-seeking procedure relies on…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
Linear maps preserving pure states of a quantum system of any dimension are characterized. This is then used to establish a structure theorem for linear maps that preserve separable pure states in multipartite systems. As an application, a…