相关论文: Real space quantum metric of solids

The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…

We propose a protocol to test whether the postulate of a measurement acting as an instantaneous projection onto an eigenstate of the measurement apparatus is compatible with physical reality. This approach is solely based on repeated…

Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…

The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…

Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…

Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings…

The paper proves that quantum mechanics is compatible with the constructive realism of modern philosophy of science. The proof is based on the observation that properties of quantum systems that are uniquely determined by their preparations…

This paper treats the isometries of metric spaces of quantum states. We consider two metrics on the set all quantum states, namely the Bures metric and the one which comes from the trace-norm. We describe all the corresponding (nonlinear)…

A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations. Instead, it is an extended object subject to tidal forces and a superposition of time dilations at…

Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…

We show that the metric (line element) is the first geometrical object to be associated to a discrete (quantum) structure of the spacetime without necessity of black hole-entropy-area arguments, in sharp contrast with other attempts in the…

We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…

Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…

In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…

The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of…

We construct noncommutative or `quantum' Riemannian geometry on the integers $\Bbb Z$ as a lattice line $\cdots\bullet_{i-1}-\bullet_i-\bullet_{i+1}\cdots$ with its natural 2-dimensional differential structure and metric given by arbitrary…

Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…

Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the…