Quantum information via state partitions and the context translation principle

Abstract

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.1 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.

Quantum hocus-pocus

“…"Forcing" a "measurement" of such states in a coherent superposition of "observables" results in a context translation [18]. This may introduce stochasticity due to the many (for all practical purposes [19]) uncontrollable degrees of freedom of the measurement device [20].…”

Noncontextuality in multipartite entanglement

“…Still other schemata [25] deny the existence of even this restricted set of contexts by maintaining that an n-ary quantum system is only capable of storing exactly one nit of quantum information. Thereby only a single context appears relevant; e.g., the context associated with the particular basis of n-dimensional Hilbert space in which this nit is encoded.…”

On Counterfactuals and Contextuality

“…Suppose it is not unreasonable to speculate about the following three assumptions [51]: As strange as the first assumption may appear, it amounts to the everyday experience that no agent, deterministic or other, can be prepared to render answers to every conceivable question. A "silly" example for this feature would be the attempt of a person to enter the question "is there enough oil in the car's engine?"…”