Foundations of quantum mechanics and their impact on contemporary society

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantisation. This approach naturally leads to the usual quantum formalism, within a new realistic conceptual framework that is discussed in details. Physically, the structure of Quantum Mechanics appears as a result of the interplay between the quantised number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to define these modalities. Mathematically, the Hilbert space structure appears as a consequence of a specific "extra-contextuality" of modalities, closely related to the hypothesis of Gleason's theorem, and consistent with its conclusions.

This talk will illustrate the relational interpretation of quantum theory, and compare the conceptual 'cost' it requires us to assume with the conceptual 'cost' demanded by the main other interpretations of the theory. It will discuss the philosophical and general implication of understanding quantum theory in this manner.

This talk will briefly review a recent derivation of quantum theory and free quantum field theory from purely information-theoretical principles, leading to an extended theory made with quantum walks. We will focus on the causality principle for quantum theory, and show that its notion coincides with the usual Einstein’s one in special relativity. It will then see how Lorentz transformations are derived from just our informational principles, without using space-time, kinematics, and mechanics. The Galileo relativity principle is translated to the case of general dynamical systems. The resulting invariance group is a nonlinear version of the Lorentz group  (the automata theory is thus a model for the so-called "doubly special relativity"), and the usual linear group is recovered in the small wavevector regime, corresponding to the physical domain experimented so far. The notion of particle is still that of Poincaré invariant. New interesting emerging features arise that have a General-Relativity flavour.

Complementarity and uncertainty were two ideas in the early development of quantum mechanics. Famously, Bohr and Heisenberg introduced them separately, after they took a break from a series of intense discussions in Copenhagen in 1927. They both worked at a rather heuristic level, and public presentations of their ideas still tend to reflect this early style and the sense of paradox, which the original authors cherished so much.

On the other hand, also in 1927, the theory took mathematical shape at the hands of von Neumann, which made wave particle dualism obsolete, and opened up the possibility of turning the heuristic ideas of Heisenberg and Bohr into general, quantitative and falsifiable statements. For uncertainty this process also began in 1927, when Kennard and Weyl fulfilled Heisenberg's promise that the uncertainty relations could be proved from the basic assumptions of the theory. The disturbance-accuracy tradeoff took much longer, but is today also firmly established. 

The role of complementarity changed in a general process of sharpening of interpretation. Today the operational content of quantum mechanics and its statistical framework is very clear. It can be applied and taught with confidence without taking recourse to Bohr's elaborate complementary doublethink. Yet the old idea still has an important if somewhat demystified place. In the talk this place will be pointed out and some continuity with origins established.

We formulate thermodynamics as an exclusive consequence of information conservation. The framework can be applied to most general situations, beyond the traditional assumptions in thermodynamics, where systems and thermal-baths could be quantum, of arbitrary sizes and even could posses inter-system correlations. Further, it does not require a priory predetermined temperature associated to a thermal-bath, which does not carry much sense for finite-size cases. Importantly, the thermal-baths and systems are not treated here differently, rather both are considered on equal footing. This leads us to introduce a "temperature"-independent formulation of thermodynamics. We rely on the fact that, for a given amount of information, measured by the von Neumann entropy, any system can be transformed to a state that possesses minimal energy. This state is known as a completely passive state that acquires a Boltzmann-Gibbs canonical form with an intrinsic temperature. We introduce the notions of bound and free energy and use them to quantify heat and work respectively. We explicitly use the information conservation as the fundamental principle of nature, and develop universal notions of equilibrium, heat and work, universal fundamental laws of thermodynamics, and Landauer's principle that connects thermodynamics and information. We demonstrate that the maximum efficiency of a quantum engine with a finite bath is in general different and smaller than that of an ideal Carnot's engine. We introduce a resource theoretic framework for our intrinsic-temperature based thermodynamics, within which we address the problem of work extraction and inter-state transformations.

Dynamics is incorporated in physical theories through conservation laws and equations of motion.  It is conventionally assumed to be an elemental part of nature – as existing without question. If, however, conservation laws and equations of motion were found to be due to a deeper cause, our understanding of time would need to be revised at a fundamental level. This talk will show how the violation of time reversal symmetry (T violation) of the kind observed in K and B meson decay might be such a cause. It will use a new quantum theory that treats time and space equally. If there is no T violation, the theory allows a material object to be localised in both space and time, i.e. the object would exist only in a small region of space and in a small interval of time. As the object would not exist before or after the time interval, there is no equation of motion and no conservation laws. The elementary assumption of dynamics is clearly absent here. However, the same formalism is dramatically different when T violation is present: the T violation makes it impossible for the object to be localized at any one time. Moreover, the object follows an equation of motion and conservation laws are obeyed. As such, dynamics emerges in the new theory as a consequence of T violation. This talk will discuss how local variations in T violation might be used to test predictions of the new theory.

In quantum mechanics, a complete set of commuting observables is the only requirement to determine the state of a quantum system. An exception to this rule holds for systems of indistinguishable identical particles where non-observable quantities (labels), that render the particles distinguishable, are introduced from the start: a procedure needing restrictions on the admissible states and observables to avoid the direct physical manifestation of the labels.

Yet when quantum correlations, in particular entanglement, among identical particles are taken into consideration, labels give rise to a spurious part of correlations. Distinguishing the latter from the real part of entanglement, which is the very resource for quantum information processing, has remained debated, notwithstanding the fact that systems employed for quantum technologies typically involve identical particles as elementary building blocks. In addition, notions ordinarily used to analyse entanglement for non-identical particles are not applicable to identical particles.

This talk will discuss a novel approach to describe identical particles in quantum mechanics where non-observable quantities are never introduced. It will show that its advantage, besides the methodological aspects, lies in the capacity of only dealing with physical entanglement. Moreover, the usual notions, such as partial trace, Schmidt decomposition and von Neumann entropy, are used to measure entanglement for both non-identical and identical particles. Finally, it will prove that this approach makes it emerge the identity of particles as a new source of operational entanglement which is directly utilizable for quantum information tasks. 

The paradigm shift that Quantum Communications represent versus classical counterpart allows envisaging the use of the qubits as a probe for fundamental tests of Quantum Mechanics and Gravity on a scale beyond terrestrial limits. We shall report on the extension of the Quantum Communications and Technologies to long distances, on the surface of the Earth as well as from the Earth to an orbiting terminal in Space. This is influenced by hurdles as the large losses, the effects on the optical propagation of the turbulent medium and the relative motion of terminals. Nevertheless, it was possible to demonstrate the Quantum Communications with Low-Earth-Orbit satellites using polarization degree of freedom to encode the qubits. This was later exteded to temporal modes of a qubit,  to demonstrate the quantum interference along a Space channel will be also described. The recent results on the extension to Space of the Gedankenexperiment proposed by John Wheeler on the wave-particle duality, then about the very nature of the quantum entities, will be described.