Related papers: Quantum Reference Frames on Homogeneous Spaces
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
A quantum physical projector is proposed for generally covariant theories which are derivable from a Lagrangian. The projector is the quantum analogue of the integral over the generators of finite one-parameter subgroups of the gauge…
Most general dynamics of an open quantum system is commonly represented by a quantum channel, which is a completely positive trace-preserving map (CPTP or Kraus map). Well-known are the representations of quantum channels by Choi matrices…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in…
In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom…
We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function…
A quantum mechanical observer might be describable as having a reference system that is a superposition of classical inertial reference frames. The present paper suggests a possible weighting function in such superpositions, determined by…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…
Ground-state fidelity (GSF) and quantum renormalization group theory (QRG) have proven useful tools in the study of quantum critical systems. Here we lay out a general, unified formalism of GSF and QRG; specifically, we propose a method to…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
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…
Frame permutation quantization (FPQ) is a new vector quantization technique using finite frames. In FPQ, a vector is encoded using a permutation source code to quantize its frame expansion. This means that the encoding is a partial ordering…
In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another…
In the quest for quantum advantage, a central question is under what conditions can classical algorithms achieve a performance comparable to quantum algorithms--a concept known as dequantization. Random Fourier features (RFFs) have…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted…