Relativistic quantum information combines the informational approach to understanding and using quantum mechanical systems – quantum information – with the relativistic view of the Universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves – effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.
Relativistic quantum information combines the informational approach to understanding and using quantum mechanical systems – quantum information – with the relativistic view of the Universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves – effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from special relativity, quantum optics, general relativity, quantum communication and quantum computation. The high level of current interest in these subjects is exemplified by the recent award of the 2012 Nobel Prize in Physics to Serge Haroche and David J Wineland for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems. It is our hope that this issue will encourage new researchers to enter this rapidly developing and exciting new field. R B Mann and T C Ralph Guest Editors
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilizing the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and ``postselected'' CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their nonlinearity and time-travel paradoxes. In particular, the ``equivalent circuit model''---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of alternate theories are identified. One such theory, the theory of ``transition probability'' CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time-travel paradoxes, the ability to distinguish nonorthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with nonlinear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.
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.
Recently, the quantum information processing power of closed timelike curves has been discussed. Because the most widely accepted model for quantum closed timelike curve interactions contains ambiguities, different authors have been able to reach radically different conclusions as to the power of such interactions. By tracing the information flow through such systems we are able to derive equivalent circuits with unique solutions, thus allowing an objective decision between the alternatives to be made. We conclude that closed timelike curves, if they exist and are well described by these simple models, would be a powerful resource for quantum information processing.
Starting from the discrete spacetime structure predicted by loop quantum gravity (LQG), this paper constructs a universal model of quantum-dot information storage and systematically explores its logical correlation with time travel. We first formulate the discreteness of spacetime at the Planck scale and argue that the discrete spectra of geometric operators (area and volume) provide a natural quantized substrate for information storage. Crucially, we do not assert a direct physical isomorphism between Planck-scale spacetime quanta and mesoscopic quantum-dot spin states—a gap of roughly 26 orders of magnitude. Instead, using renormalization-group (RG) ideas and scale invariance, we reframe the link as a topological isomorphism of information structure and, operationally, as a quantum simulation: a quantum-dot array is a laboratory simulator of the discrete-spacetime information network rather than a physical counterpart of Planck-scale atoms. To address the causal paradoxes of closed timelike curves (CTCs), we propose a quantum-information self-consistency principle and connect it to Deutsch’s D-CTC model (1991; density-matrix fixed point) and the Lloyd et al. P-CTC model (2011; post-selected CTCs). We argue that spacetime discreteness supplies a natural ultraviolet cutoff which, together with non-local (entanglement-based) storage in the dot network, dissolves the grandfather paradox at the level of information. The metaphysical “isomorphism claim” is sharpened into a falsifiable “same-universality-class” hypothesis, accompanied by concrete criteria (entanglement-entropy scaling, power-law exponents, topological entanglement entropy). The proposed quantum-dot loop experiment is clarified as a quantum simulation of the information-propagation logic of CTCs, in the same paradigm as the Sycamore traversable-wormhole experiment (Jafferis et al., 2022), and is not a realization of macroscopic time travel. Building on the above, this paper advances two core theoretical constructs, each developed in a dedicated chapter. The first is the quantum-dot information-extension model (Chapter 8): the existence of a piece of spacetime information is identified with the existence of a timelike information world-tube—when information is created at an event, the quantum point carrying it extends along a timelike direction into a world-tube that persists until the information is erased. From this picture we derive a conservation law for the active quantum-point number density, a holographic–persistence capacity bound for the world-tube cross-section, and the thermodynamic costs of information creation, persistence, and annihilation. The second is the information dynamics of time travel (Chapter 9): within the world-tube language, two self-consistent routes for returning to the past are proposed—jumping to a parallel branch universe that already possesses a time machine (memory fully retained), or rewinding along one's own world-tube so that the extended quantum point recedes and annihilates at its initial event (entailing invalidation of downstream information, merging of the future and past operators' information, and the impossibility of retaining future memory). The two routes correspond respectively to cross-branch and same-branch fixed points of the causal-consistency functional. We emphasize that the pictures of Chapters 8 and 9 are theoretical hypotheses and conjectures proposed herein, intended to provide a mathematically self-consistent and in-principle falsifiable analytical framework rather than a claim about the physical realizability of time machines.
Relativistic quantum information is one of the most exciting fields of physics today. Not only does it open possibilities for new forms of computing but it also calls into question the peaceful coexistence between classical space–time and quantum physics with scenarios that reopen the relationships between locality and nonlocality in the foundational structure of physics. Curated by two international experts Ignazio Licata and Fabrizio Tamburini, this volume hosts a selection of particularly significant essays for the new territories, and is dedicated to the 60th anniversary of Prof. Ignazio Licata.