The experience from Quantum Information of the last twenty years has lead theorists to look at Quantum Theory and the whole of Physics from a different angle. A new information-theoretic paradigm is emerging, long time ago prophesied by John Archibald Wheeler with his popular coinage 'It from bit'. Theoretical groups are now addressing the problem of deriving Quantum Theory from informational principles, and similar lines are investigated in new approaches to Quantum Gravity. In my talk I will review some recent advances on these lines. The general idea synthesizing the new paradigm is that there is only Quantum Theory (without quantization rules): the whole Physics--including space-time and relativity--is emergent from quantum-information processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. The review is divided into the following parts: (a) The informational axiomatization of Quantum Theory; (b) How space-time and relativistic covariance emerge from the quantum computation; (c) What is the information-theoretical meaning of inertial mass and Planck constant, and how the quantum field emerges; (d) Observational consequences: mass-dependent refraction index of vacuum. I then conclude with some possible future research lines.
The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information‐theoretical paradigm—It from Bit— prophesied by John Archibald Wheeler is relentlessly advancing. Recently it has been shown that QT is derivable from pure informational principles. The possibility that there is only QT at the foundations of Physics has been then considered, with space‐time, Relativity, quantization rules and Quantum Field Theory (QFT) emerging from a quantum‐information processing. The resulting theory is a discrete version of QFT with automatic relativistic invariance, and without fields, Hamiltonian, and quantization rules. In this paper I review some recent advances on these lines. In particular: i) How space‐time and relativistic covariance emerge from the quantum computation; ii) The derivation of the Dirac equation as free information flow, without imposing Lorentz covariance; iii) the information‐theoretical meaning of inertial mass and Planck constant; iv) An observable consequence of the theory: a mass‐dependent refraction index of vacuum. I will then conclude with two possible routes to Quantum Gravity.
Abstract The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.
The theory is based on a new hypothesis on the nature of matter. This hypothesis is that the elementary particles, atoms, and molecules we have found in nature are not part of the real world, but constitute information about the real world. They are the wave components of a generalized Fourier analysis of our observations (which in the final analysis are always space-time distributions of photon- or particle-counter clicks). This Fourier analysis should be so general that every observation can be expressed in its terms; it thereby becomes axiomatic. Physicists of past generations, with their sound instincts, were intuitively approaching this most general and most powerful possible analysis of our observations. With the discovery of quantum mechanics, this development had advanced so far that the precise formulation of this ultimate analysis could be guessed. The model which can guide us to this mathematical formulation is that of an ideal optical observation on a physical object. This observation is made by illuminating the object with a finite number of laser beams of known amplitude and phase, and observing the amplitude and phase of the finite number of light beams emerging from the object space. The assumption that this is all the information we can ever obtain about the object leads to a wave function of the object which consists of light waves, extrapolated from the photon detectors back to the object space. It is suggested that these light waves should be presented as a product of amplitudes in a
4n-dimensional space, where
n is the number of light quanta in the signal. Most important, force, or interaction, can then be described as a linear transformation in this space. The actual mathematical formalism proposed on the basis of that model is
Xf=dtitdf.
X is the Hamiltonian of the whole universe with ${n}_{0}\ensuremath{\cong}{10}^{80}$ particles. It is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ linear matrix operator.
f is a
4n0-component vector wave function representing waves traveling at the speed of light. The coordinates are the homogeneous coordinates (
xj,yj,zj,uj) of the
n0 particles in the closed universe. The eigenvalue $\ensuremath{\omega}$, in $Xf=\ensuremath{\omega}f$, is a $4{n}_{0}\ifmmode\times\else\texttimes\fi{}4{n}_{0}$ Hermitian matrix. It can be divided into ${n}_{0}\ifmmode\times\else\texttimes\fi{}{n}_{0}$, 4 \ifmmode\times\else\texttimes\fi{} 4 submatrices, each representing a complete set of dynamic and inertial quantities of elementary particles, or interaction quanta between particles. $\frac{\mathrm{it}df}{\mathrm{dt}}=\ensuremath{\omega}f$ is therefore a complete expression of the dynamic conservation laws. A special orthogonal transformation ${\ensuremath{\alpha}}_{0}$ transforms the solution into a standard solution with eigenvalue ${\ensuremath{\omega}}_{0}$, representing
n0 identical elementary particles. The assumption that the universe is of maximum probability then leads to simple explicit expressions for all matrix elements of ${\ensuremath{\omega}}_{0}$. This means that the energy levels of all
n-particle systems (atoms or molecules) of the theory can be directly calculated. The equations demand relations between cosmological constants and atomic constants. In a universe of the size and mass of our observed universe, the elementary particle would have to be the size of the proton.
Quantum Mechanics has taught us a lesson that goes well beyond a set of new physical laws. It has provided us with genuine “theorems of epistemology”. We now know that there are situations when the observation of the world cannot be considered as the mere reading of a reality pre-existing the observation, whereas there are circumstances where the knowledge of the whole do not corresponds to the knowledge of the parts (holism). We know that there are incompatible properties that are complementary. We know that there exist properties of the whole that are incompatible with any property of each part. The notion of “object” defined in terms of its “properties ” is in contrast with its mereologic connotation according to which objects can be composed to form new objects. The particle ontology as localizable unity is in contrast with the Malament theorem in quantum field theory. To the above add the fact that the two more general fundamental theories in physics – the quantum theory of fields and the general relativity of Einstein – are logically incompatible. In order to reconcile the logical coherence of the observations with their theoretical explanation we need a radical change of paradigm. The solution here proposed is to abandon the vision of the world as a “mechanism” and to substitute it with that of “algorithm”. This is the paradigm of the “universe as a huge computer” that have been latent within the community since Richard Feynman, and nowadays is resurrecting in physics, showing its full theoretical power. In the new algorithmic vision the “mechanics” becomes an emergent phenomenology. Without the need of physical primitive, the new “informational” program allows us to found physics on solid axiomatic grounds. The quantum theory of abstract systems along with the free quantum field theory are derived from information-theoretic axioms. The axioms of quantum theory all have an epistemological connotation, and pertain the possibility of falsifying the propositions of the theory. They reconnect holism with reductionism, probabilism and falsifiability, substituting the notion of “object” with that of “system” and of “event”, and logically implying the theorem of quantum theory without the need of using the abstract Hilbert-spaces toolkit. The free quantum field theory (Weyl, Dirac e Maxwell) is obtained by adding axioms of minimization of algorithmic complexity. The informational framework well separates the notions of “experiment”and “theory”: the theory connects input with output, the experiment being identified with the collection of input, output, and objective intermediate events. The objective reality (experiment) is made of “icons” with which we interact: the theory is the underlying algorithm. The paradigm describes the tapestry of reality as pure software, “software”. “Software without hardware”: the dematerialization of physics. “Reality without realism” means pure logical coherentism.
Quantum information theory represents a revolutionary paradigm that merges quantum mechanics with information science, fundamentally transforming our understanding of computation, communication, and information processing. This chapter provides a comprehensive examination of quantum information theory, exploring its theoretical foundations, practical applications, and transformative potential across multiple domains. We investigate the core principles including quantum bits (qubits), superposition, entanglement, and quantum interference, while analyzing their implications for quantum computing, cryptography, and communication protocols. Through systematic literature review and methodological analysis, we present current research trends, breakthrough developments, and emerging applications. The chapter addresses significant challenges including decoherence, error correction, and scalability issues that currently limit practical implementation. Our discussion encompasses quantum algorithms, quantum error correction codes, and the evolving landscape of quantum technologies. We conclude by identifying future research directions and the potential societal impact of quantum information systems, emphasizing both the unprecedented opportunities and the technical obstacles that define this rapidly advancing field.