We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.
We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.
We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, which encompasses linear optical quantum computing.
The relativistic second quantization of free bosons is extended to fermions. To know how relativistic creation and annihilation operators operate on bra and ket vectors, it is necessary to have a relativistic scalar product which in the case of free particles can be constructed. For particles interacting with each other or capable of emitting and absorbing particles of the same kind, it is pointed out that adequate wave equations for an indefinite number of particles each taking a separate time coordinate have not yet been found and so no scalar product can be found. Thus creation and annihilation operators can be defined only by their operation on a bra vector or a ket vector but not by both. With the help of these, the relativistic wave equations referred to above are proposed and their consistency conditions studied. For the particular case of scalar particles, an illustration is given that such a theory may admit certain expressions as probabilities.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.
Relativistic quantum information investigates the interplay between quantum mechanics and relativity and is becoming increasingly relevant for future quantum technologies operating over large distances or in gravitational fields. This dissertation studies how relativistic effects influence the storage, transmission, and interference of quantum states of light, with particular emphasis on quantum memories and frequency-entangled photons. A theoretical framework is developed to describe relativistic transformations of photonic quantum states and their interaction with realistic quantum memories. Special attention is given to the influence of gravitational redshift and relativistic motion on quantum coherence, entanglement, and Hong–Ou–Mandel interference. The resulting models provide quantitative predictions for experimentally accessible scenarios and identify conditions under which relativistic effects become relevant for quantum communication and distributed quantum information processing. The presented results contribute to the emerging field of relativistic quantum information by connecting concepts from quantum optics, quantum communication, and general relativity. Beyond their fundamental significance, they provide theoretical tools for the development of future space-based quantum networks and relativistic quantum technologies. Beyond the results presented in this dissertation, the developed framework points toward a broader research program centered on the **Nonlinear Separability Problem**. This problem is proposed as a unifying mathematical perspective for investigating the limits of distinguishability, classification, and information processing in both classical and quantum systems. Its formulation naturally connects to a wide range of contemporary research areas, including computational complexity theory (e.g., P versus NP), quantum information processing, machine learning, optimization, information theory, quantum foundations, and mathematical physics. In particular, the framework suggests new approaches to studying the role of nonlinearity in quantum state discrimination, quantum communication protocols, and the mathematical structure of high-dimensional information spaces. While many of these directions remain to be explored, the present work establishes a conceptual and mathematical basis for future investigations. It is anticipated that further development of the Nonlinear Separability Problem may contribute to a deeper understanding of fundamental questions across mathematics, computer science, and quantum technologies, thereby opening new interdisciplinary avenues of research.
We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the mode decompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration. We show that the amount of generated entanglement can be magnified by initial single-mode squeezing, for which we provide an explicit formula. Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed.
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schrödinger equation of a spinless particle exposed to an external electromagnetic field is obtained.