We consider the process of changing reference frames in the case where the reference frames are quantum systems. We find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these frames. We explore this process with examples involving reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.
We consider the process of changing reference frames in the case where the reference frames are quantum systems. We find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these frames. We explore this process with examples involving reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, the process of changing reference frames is considered for the case where the reference frames are quantum systems. As part of this process, it is shown that decoherence is necessarily induced on any quantum system described relative to these frames. This process is explored using examples involving quantum reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.
Reference frames are of special importance in physics. They are usually considered to be idealized entities. However, in most situations, e.g. in laboratories, physical processes are described within reference frames constituted by physical systems. As new technological developments make it possible to demonstrate quantum properties of complex objects an interesting conceptual problem arises: Could one use states of quantum systems to define reference frames? Recently such a framework has been introduced in [F. Giacomini, E. Castro-Ruiz, and Č. Brukner, Nat Commun 10, 494 (2019)]. One of its consequences is the fact that quantum correlations depend on a physical state of an observers reference frame. The aim of this work is to examine the dynamical aspect of this phenomena and show that the same is true for correlations established during an evolution of a composite systems. Therefore, decoherence process is also relative: For some observers the reduced evolution of subsystems is unitary, whereas for others not. I also discuss implications of this results for modern developments of decoherence theory: Quantum Darwinism and Spectrum Broadcast Structures.
The concept of a reference frame has been a part of the physical formalism since the early days of physics. The reference frame was always understood as a physical system with respect to which states of other physical systems are described. With the adoption of quantum theory, our understanding of physical systems has fundamentally changed, yet we still rely on classical systems for the definition of reference frames. If we acknowledge the fact that all systems are quantum mechanical, including reference frames, then we have to be able to describe quantum systems relative to other quantum systems. \n \nIn this thesis we develop a framework for integrating quantum reference frames into the formalism of quantum mechanics. We show how the description of states and measurements has to be refined in order to account for the quantum nature of the reference frame. Initially, we study the implications of the new description with a quantum reference frame associated with a generic compact group. Then, we apply the same approach to the study of relativistic quantum reference frames associated with the Poincaré group, which is not compact. \n \nOur findings for the generic compact group include an analysis of how well a quantum system defines a frame of reference for other systems. Also in the generic case we analyze the effects of a measurement on a quantum reference frame. In the relativistic case we first find how the massive representations of the Poincaré group decompose into irreducible representations. This is a key problem in the analysis of quantum reference frames. Finally, we analyze a relativistic quantum reference frame that is used for measuring the total momentum. We will show how the relativistic measurements of total momentum should be described with respect to a quantum reference frame. We will also show how these measurements affect the quantum reference frame.
Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al, Quantum 4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory - the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.
Abstract The subject of quantum reference frame transformations gets popular lately with some interesting new theoretical development partly for the reason that the physics involved is becoming experimentally accessible. The position of a position eigenstate when observed from an object with ‘uncertainty’ in position would be seen with ‘uncertainty’. In fact, even the existence of entanglement is reference frame-dependent. We present an improved formulation of such a transformation and give a novel way to describe exactly by ‘how much’ the ‘value of the position’ has changed which fully encodes all information about the changes, including the ‘uncertainty’ and entanglement. That is an application of the notion of noncommutative values of physical quantities we introduced to understand the reality of quantum physics and beyond. Some implications on fundamental physics will also be discussed. In particular, we suggest thinking about quantum gravity as a theory of general quantum relativity, alleviating Penrose’s notion of incompatibility of qauntum mechanics with the relativity principle.
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the ‘value’ of an observable for a fixed state change. That is the exact analog of the classical description, for example, of the value of the x-coordinate for a particle decrease by 2 units when we perform a translation of the reference frame putting the new origin at x=2. The essence of the quantum reference frame transformations is to have the quantum fluctuations, and even entanglement, of the physical object which serves as the (new) reference frame, taken into account. We illustrate how the recently introduced notion of the noncommutative values of quantum observables gives such a definite description successfully. Formulations, and an analysis of a case example in qubit systems, of analog transformations for observables with a discrete or finite spectrum is also presented. Issues about the evolving picture of the symmetry system of all quantum reference frame transformations discussed.