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We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result…
In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states:…
Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the $L^2$ Wasserstein distance of…
Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…
The Shannon entropy of a collection of random variables is subject to a number of constraints, the best-known examples being monotonicity and strong subadditivity. It remains an open question to decide which of these "laws of information…
We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there…
Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: entanglement reflects non-local correlations, while nonstabilizerness quantifies the deviation from…
Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…
In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum…
Nonstabilizerness or `magic' is a crucial resource for quantum computers which can be distilled from noisy quantum states. However, determining the magic of mixed quantum has been a notoriously difficult task. Here, we provide efficient…
We give a new algorithm for computing the robustness of magic - a measure of the utility of quantum states as a computational resource. Our work is motivated by the magic state model of fault-tolerant quantum computation. In this model, all…
Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of…
The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when…
Characterizing quantum magic -- the resource enabling computational advantage beyond stabilizer circuits -- is subtle in qubit systems because established measures can give conflicting information about the same state. We introduce C(rho),…
Quantum many-body systems display an extraordinary degree of complexity, yet many of their features are universal: they depend not on microscopic details, but on a few fundamental physical aspects such as symmetries. A central challenge is…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…
In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an…
The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…
Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity…