Related papers: From Geometric Quantum Mechanics to Quantum Inform…
In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme chosen, and monotone quantum metrics on the…
We explore the important fundamental question of how quantum information is localized in quantum gravity, in a perturbative approach. Familiar descriptions of localization of information, such as via tensor factorization of the Hilbert…
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…
We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
The natural gradient is central in neural quantum states optimizations but it is limited by the cost of computing and inverting the quantum geometric tensor, the quantum analogue of the Fisher information matrix. We introduce a…
We provide evidence that quantum mechanics can be interpreted as a rational algorithm for finding the least complex description for the correlations in the outputs of sensors in a large array. In particular, by comparing the…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
Presented is a quantum gravity theory that is a quantum mechanical generalization of Einstein's vierbein field-based approach, where the classical metric tensor field is promoted to a quantum mechanical metric tensor field operator. The…
We discuss a quantum mechanical indirect measurement method to recover a position dependent Hamilton matrix from time evolution of coherent quantum mechanical states through an object. A mathematical formulation of this inverse problem…
The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the…
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
The Fubini product of operator spaces provide a powerful tool for analysing properties of tensor products. In this paper we review the the theory of Fubini products and apply it to the problem of computing invariant parts of dynamical…
We consider a hybrid bimetric model where, in addition to the ordinary metric tensor that determines geometry, an informational metric is introduced to describe the reference frame of an observer. We note that the local information metric…
The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the…