What Is “System”: The Information-Theoretic Arguments

Abstract

The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of mutually non-interacting, nonentangled systems to employ entanglement of the newly defined "(sub)systems" consisting the one and the same composite system. Given the different divisions of a composite system into "subsystems", the Hamiltonian of the system may generate in general non-equivalent quantum computations. Redefinition of "subsystems" of a composite system may be regarded as a method for avoiding decoherence in the quantum hardware. In principle, all the notions refer to a composite system as simple as the hydrogen atom.

The Ghostly Quantum Worlds

“…However, only recently we have started to realize the related subtleties appearing in the quantum mechanical context. The following general observation is in order (Dugić and Jeknić, 2006;Dugić and Jeknić-Dugić, 2008 ;Jeknić-Dugić et al, 2011;Jeknić-Dugić et al, 2012): …”

“…Nevertheless, the set of the degrees of freedom is not unique. One can perform the different kinds and types of the variables transformations to obtain the alternate set of the degrees of freedom that formally define the different structures of the composite system  (Dugić and Jeknić, 2006;Dugić and Jeknić-Dugić, 2008;Jeknić-Dugić et al, 2011;Jeknić-Dugić et al, 2012).…”

“…To simplify notation, we denote formally the structure we belong to by   . Now we consider the different, mutually irreducible structures of the Universe, formally denoted as the set { } i  , whose existence is at least formally guaranteed (Dugić and Jeknić, 2006;Dugić and Jeknić-Dugić, 2008;Jeknić-Dugić et al, 2011;Jeknić-Dugić et al, 2012).…”

“…Our starting point is the recently rediscovered importance of the "structure", i.e., of the decomposition into parts, subsystems, of a composite quantum system (Dugić and Jeknić, 2006;Dugić and Jeknić-Dugić, 2008;Jeknić-Dugić et al, 2011;Jeknić-Dugić et al, 2012). When applied to the quantum Universe, this opens the new avenues not only for interpretation but also a wide-range of implications for describing the quantum Universe.…”

Complete Positivity on the Subsystems Level

“…The open quantum systems theory [1,2] is at the core of the modern quantum theory and applications, ranging from the foundational issues [1][2][3][4][5][6][7][8] and quantum optics [1,9] to the cosmological issues [10,11] and the diverse applications, e.g., in quantum technology [12], materials science [13], chemistry and nanotechnology [14][15][16][17] as well as in the nascent field of quantum thermodynamics [18,19].…”