Related papers: Monotone metric tensors in Quantum Information Geo…
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
Quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We develop the BFGS algorithm to study…
Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The motion of a quantum particle constrained to a two-dimensional non-compact Riemannian manifold with non-trivial metric can be described by a flat-space Schroedinger-type equation at the cost of introducing local mass and metric and…
To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike…
We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. That is, by considering phase space probability distributions parametrized by the covariances and supplying…
The concept of coherence is one of cornerstones in physics. The development of quantum information science has lead to renewed interest in properly approaching the coherence at the quantum level. Various measures could be proposed to…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite.…
We study information theoretic geometry in time dependent quantum mechanical systems. First, we discuss global properties of the parameter manifold for two level systems exemplified by i) Rabi oscillations and ii) quenching dynamics of the…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…