The study of quantum resources in the relativistic limit has attracted attention over the last couple of decades, mostly due to the observation that the spin-momentum entanglement is not Lorentz covariant. In this work, we take the investigations of relativistic quantum information a step further, bringing the foundational question of realism to the discussion. In particular, we examine whether Lorentz boosts can affect quantum irrealism-an instance related to the violations imposed by quantum mechanics onto a certain notion of realism. To this end, we adopt as a theoretical platform a model of a relativistic particle traveling through a Mach-Zehnder interferometer. We then compare the quantum irrealism assessed from two different inertial frames in relative motion. In consonance with recent findings in the context of quantum reference frames, our results suggest that the notion of physical realism is not absolute.
The study of quantum resources in the relativistic limit has attracted attention over the last couple of decades, mostly due to the observation that the spin-momentum entanglement is not Lorentz covariant. In this work, we take the investigations of relativistic quantum information a step further, bringing the foundational question of realism to the discussion. In particular, we examine whether Lorentz boosts can affect quantum irrealism-an instance related to the violations imposed by quantum mechanics onto a certain notion of realism. To this end, we adopt as a theoretical platform a model of a relativistic particle traveling through a Mach-Zehnder interferometer. We then compare the quantum irrealism assessed from two different inertial frames in relative motion. In consonance with recent findings in the context of quantum reference frames, our results suggest that the notion of physical realism is not absolute.
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF transformations for Lorentz symmetry is still lacking. The present work aims to fill this gap. We first introduce a reformulation of relativistic quantum mechanics independent of any notion of preferred temporal slicing. Based on this, we define transformations that switch between the perspectives of different relativistic QRFs. We introduce a notion of ''quantum Lorentz transformations'' and ''superposition of Lorentz boosts'', acting on the external degrees of freedom of a quantum particle. We analyse two effects, superposition of time dilations and superposition of length contractions, that arise only if the reference frames exhibit both relativistic and quantum-mechanical features. Finally, we discuss how the effects could be observed by measuring the wave-packet extensions from relativistic QRFs.
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.
Abstract Particles cannot travel faster than the speed of light, nor can information. Nonetheless, this assumption has been frequently questioned over the years. This includes radical proposals like tachyons that can be observed in particle accelerators to more subtle ideas like studying superluminal causation to find classical explanations for quantum correlations. Most recently, it has been argued (Dragan and Ekert 2020 New J. Phys. 22 033038) that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. A consequence of this resolution is that different observers no longer agree whether a particle is incoming or outgoing or in a superposition of the two. We further find a similar apparent paradox for the entropy and/or temperature under superluminal Lorentz boosts and resolve it in an analogous fashion. Finally, we discuss Bell experiments under superluminal quantum reference frame transformations, showing that the involved probabilities still remain conserved. By applying the toolbox of quantum reference frames, we start charting an unexplored territory of superpositions between sub-and-superluminal quantum observers which gives rise to new conceptual questions.
While particles cannot travel faster than the speed of light, nor can information, this assumption has over the years been frequently questioned. Most recently, it has been argued [New J. Phys. 22, 033038 (2020)] that in a world with superluminal observers local determinism is impossible, linking the two pillars of physics-quantum theory and relativity-suggesting that the latter serves as the foundation for the former. Motivated by this approach, in this work, we extend the framework of quantum reference frames to incorporate superluminal Lorentz transformations. We apply this conceptual result to examine an apparent paradox where particles acquire negative energies after undergoing a superluminal Lorentz boost and propose a resolution within our framework. We also discuss Bell experiments under superluminal quantum reference frame transformations, showing that involved probabilities remain conserved.
The developments of special relativity and quantum mechanics marked beginning of modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity---the space-time interval---whose value all inertial observers agree upon. This reveals, so to speak, a genuine fact of universe, a relativistic invariant. On other hand, since dawn of quantum mechanics, there is no consensus on what theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and very notions of and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between the observer and the observed and employ notion of quantum reference frame. Unitary transformations then follow that allow us to perceive physical resources seen from viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that notion of physical reality implied by quantum mechanics is not absolute.