Related papers: Information geometry in quantum field theory: less…
The quantum metric, a geometric measure of state-space distance, has recently attracted growing attention for capturing anomalous state responses to parameter variations. Especially in non-Hermitian systems, the quantum metric has been…
One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which…
Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…
We consider the geometry of quantum states associated with different classes of random matrix Hamiltonians, in particular ensembles that show integrability to chaotic transition in terms of the nearest neighbour energy level spacing…
We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
We present two examples of non-trivial field theories which are scale invariant, but not conformally invariant. This is done by placing certain field theories, which are conformally invariant in flat space, onto curved backgrounds of a…
The equilibration of matter and onset of hydrodynamics can be understood in the AdS/CFT context as a gravitational collapse process, in which "collision debris" create a horizon. In this paper we consider the simplest geometry possible, a…
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
The cosmological horizon has an associated entropy suggesting that it might encode a quantum mechanical system on its surface. This has motivated extending the principles of the anti-de Sitter (AdS) space/ conformal field theory (CFT)…
It is a well-studied phenomenon in AdS$_3$/CFT$_2$ that pure states often appear 'too thermal' in the classical gravity limit, leading to a version of the information puzzle. One example is the case of a heavy scalar primary state, whose…
Establishing consistent and dense correspondences across multiple images is crucial for Structure from Motion (SfM) systems. Significant view changes, such as air-to-ground with very sparse view overlap, pose an even greater challenge to…
A central conjecture in quantum gravity is the non-existence of global symmetries. As a fully unitary theory, there is no information loss in a UV complete quantum gravity theory. We see both these concepts reflected in the AdS/CFT…
In this short note, we examine geodesic distance in Fisher information space in which the metric is defined by the entanglement entropy in CFT_(1+1). It is obvious in this case that the geodesic distance at a constant time is a function of…
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…
The presence of symmetries imposes a stringent set of constraints on a system. This constrained structure allows intelligent agents interacting with such a system to drastically improve the efficiency of learning and generalization, through…
Understanding quantum correlations through information-theoretic measures is fundamental to developments in quantum field theory, quantum information, and quantum many-body physics. A central feature in a plethora of systems is the area…