Dear Colleagues,

Among the many symmetries present in all physical theories, one of the deepest and most fundamental is the one contained in the postulate that the time evolution of a closed quantum system is described by a unitary transformation of the initial state. Thus, the complete reversibility of, at least in principle, all the processes described by the laws of quantum mechanics is established.

At the same time, there is an obvious conflict of the mentioned postulate with the observation that, for all practical purposes, each quantum measurement necessarily leads to a projection of the previous quantum state on one of the eigenvalues ​​of the observable under consideration. From this follows the loss of all other features of this quantum state and, consequently, loss of the reversibility and time symmetry of the quantum evolution. One of the leading approaches to solving the above tension is the theory of decoherence and quantum Darwinism, explaining the emergence of classical information and irreversibility in individual subsystems while maintaining the unitarity of the evolution of the complete system.

Quantum Darwinism, as demonstrated by W. Żurek, also showed the role of symmetry in the derivation of Born's Rule together with the additivity of the probabilities, using a mechanism called entanglement-assisted invariance or envariance. For this purpose, the symmetry of entangled quantum states alone has proved to be sufficient, without resorting to decoherence theory tools, such as partial traces of density matrices. Żurek referred to Laplace's intuition, stating that the symmetry of elementary events implies the identity of their probabilities. As a result, Żurek, based solely on symmetry considerations, showed irrelevance of phases for local states, thus implying decoherence, and was also able to explain the nature of quantum jumps.

In quantum Darwinism, the basis for defining the objectivity of observation is the symmetry between individual observers, for which the possibility of independent and identical access to classical information about the measurement result is postulated. Moreover, recently, another kind of symmetry called strong symmetry, phrasing equivalence between the different ways of coding classical information, proved to be a sufficient condition for the occurrence of some form of quantum Darwinism.

One should also bear in mind the fact that assumptions regarding their symmetry are of great practical importance for the study of decoherence models and information flow. Due to the high complexity of the macroscopic systems needed to demonstrate quantum Darwinism, virtually all information flow scenarios studied so far had to refer to systems with high symmetry to simplify the calculations.

In this Special Issue, we want to take a closer look at how new considerations based on recognizing or applying symmetry can contribute to the deepening of the understanding and development of quantum Darwinism. The considerations will concern both the identification of new places in the theory where symmetries have not been found so far, as well as propositions on how methods based on symmetrization or the assumption of certain symmetries may lead to the widening of the scope of the studied phenomena within quantum Darwinism.

Dr. Piotr Mironowicz
Guest Editor

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• quantum Darwinism
• symmetries
• quantum information
• classical information
• fundamentals of quantum mechanics
• decoherence
• quantum jumps
• quantum open systems