For many-particle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of n-ary ( joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of single outcomes, a context translation principle is proposed. Quantum randomness is related to the uncontrollable degrees of freedom of the measurement interface, thereby translating a mismatch between the state prepared and the state measured.
Information in many-particle quantum systemsThe preparation of a single particle n-state quantum system in a single state constitutes the operationalization of a nit, or qunit. Likewise, the occurrence of an outcome of an observable with n possible outcomes can be associated with accessing a nit of information. For a single particle observable, this is associated with choosing a vector from an orthogonal basis of n-dimensional Hilbert space. In the many-particle case, nits may not only be localized at single particle observables, since due to entanglement, the nits may be distributed over the particles by representing joint particle properties.In what follows we shall review and extend formal generalizations [1, 2] of the single particle two-state case to an arbitrary finite number of particles with an arbitrary finite number of different measurement outcomes per particle. Thereby, we define a nit as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables. We shall demonstrate the following property: k particles specify k nits in such a way that k measurements of comeasurable observables with n possible outcomes are necessary to determine the information. Stated pointedly, k particles can carry k nits.Conceptually, such properties have been previously proposed by Zeilinger [3] as a foundational principle for quantum mechanics. Zeilinger merely considered two-state systems of two and three particles, yet an informal hint for higherdimensional single quantum systems is in footnote 6 of [3] on p. 635. There is a slight difference in the approach of Zeilinger and the author: whereas here the logico-algebraic properties are studied 'top-down' by assuming Hilbert space quantum mechanics and arriving at the foundational principle purely deductively, Brukner and Zeilinger [4] reconstruct certain features of quantum physics by treating this principle 'bottom-up' as an axiom.