Toolbox for reconstructing quantum theory from rules on information acquisition

Abstract

We develop an operational approach for reconstructing the quantum theory of qubit systems from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's 'catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions. Four rules are imposed, asserting (1)

Quantum theory from questions

“…These results highlight information as a 'charge of quantum theory' and the benefits of this informational approach. This work emphasizes the sufficiency of restricting to an observer's information to reconstruct the theory and completes the quantum reconstruction initiated in [1]. …”

“…To this end, we shall exhibit, using the novel framework developed in [1], how the quantum formalism can be constructively and explicitly derived from simple operationally comprehensible rules which restrict an observer's acquisition of information about systems he is observing. The acquisition of information of the observer about the systems will proceed by interrogation with binary questions.…”

“…In particular, we take the quantum state to represent the observer's 'catalogue of knowledge' about the observed system(s), rather than an intrinsic state of the latter. This is conceptually motivated by and in line with the relational interpretation of quantum mechanics [1,10,[36][37][38], the informational interpretation in [11,12,14,16] and (at least elements of) QBism [39][40][41]. While this general philosophy goes back to Rovelli's seminal relational quantum mechanics [10], none of these earlier works provide a concrete framework from which to reconstruct the theory.…”

“…While this general philosophy goes back to Rovelli's seminal relational quantum mechanics [10], none of these earlier works provide a concrete framework from which to reconstruct the theory. This is a shortcoming which has been overcome in [1] and which will be exploited in the sequel. As such, the present manuscript (together with [1]) can be viewed as a completion -in the context of qubit systems -of many of the ideas put forward in these earlier works and, in particular, of relational quantum theory [10].…”

“…This is a shortcoming which has been overcome in [1] and which will be exploited in the sequel. As such, the present manuscript (together with [1]) can be viewed as a completion -in the context of qubit systems -of many of the ideas put forward in these earlier works and, in particular, of relational quantum theory [10].…”