Related papers: Gauge Invariance and the Quantum Metric Tensor

Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…

We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…

Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems,…

We develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. A qubit has dependence on a 1-qubit unitary…

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…

Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This…

In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…

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…

We propose a generic protocol to experimentally measure the quantum metric tensor, a fundamental geometric property of quantum states. Our method is based on the observation that the excitation rate of a quantum state directly relates to…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach…

We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…

Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…

In this review we look into the gauge-dependence of scalar-induced gravitational waves (SIGWs) that are second-order tensors produced by first-order scalar-modes. The method includes deriving the background, first- and second-order Einstein…

The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…

It is well established that quantum criticality is one of the most intriguing phenomena which signals the presence of new states of matter. Without prior knowledge of the local order parameter, the quantum information metric (or fidelity…

The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…

Quantum metrology uses small changes in the output probabilities of a quantum measurement to estimate the magnitude of a weak interaction with the system. The sensitivity of this procedure depends on the relation between the input state,…

Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…