Related papers: Gauge Invariance and the Quantum Metric Tensor
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
The quantum geometric potential is a gauge invariant carrying novel geometric features between any two energy levels or bands in quantum systems. In generic time-dependent systems it gives a vital physical modification for the instantaneous…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family…
As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
Measurement-Based Quantum Computation (MBQC) is a model of quantum computation, which uses local measurements instead of unitary gates. Here we explain that the MBQC procedure has a fundamental basis in an underlying gauge theory. This…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
Quantum Metrology is one of the most promising application of quantum technologies. The aim of this research field is the estimation of unknown parameters exploiting quantum resources, whose application can lead to enhanced performances…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular…
Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
We derive a relation between four-fermion QED Green functions of different covariant gauges which defines the gauge dependence completely. We use the derived gauge dependence to check the gauge invariance of atom-like bound state…