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. 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.

Quantum Randomness is Chimeric

“…In the physical measurement process, it is the question of how, through “mediation” of its environment and the measurement apparatus, a physical state or system which initially is unprepared to answer a particular query—or, stated differently, is value indefinite and chimeric—“translates” the respective “detuned” query such that it is can respond to the request. Through this “context translation”, it may have acquired signals and information exterior to itself, which may render the answer stochastic relative to itself (because of an influx from the open environment) and to the experimental means available [ 63 , 64 ] (containing or severing that open environment).…”

“…This is problematic as the corresponding experimental protocols (“prepare a pure state and measure a different one”) seem to suggest that they “reveal” some pre-existing property—indicated by the (non)occurrence of a detector click. This could be misleading, as the respective click might either be subject to debate and interpretation or merely signify the capacity of the measurement apparatus to “translate an improper question;” introducing stochastic noise [ 63 ]. (A debate [ 161 , 162 ] on the alleged “ a posteriori teleportation” is an example for such a nonunique semantic perception of syntactically undisputed detector clicks.)…”

Quantum Violation of the Suppes-Zanotti Inequalities and “Contextuality”

“…But if there is a mismatch between preparation and measurement, the latter environment distorts value definiteness by an "inflow" of information from "outside of" the object. Consequently, it makes no sense to speak of any such measurement result as "being an element of physical reality" associated with the observed system alone -one has to add the (open) environment which "translates" the preparation into the measurement, thereby introducing (external with respect to the object) noise [67,70].…”

Vector computation

“…Nevertheless, even in this reduced scheme of parallelism, it might be possible to formulate relational queries corresponding to useful information by appropriate partitioning of the state space. [52][53][54] We may formulate the fundamental problem of intrinsically operational vector encoding of a computation aka quantum computation: under what circumstances is it possible to derive "useful" information about (the components) of a vector? It is not too unreasonable to suspect that an answer to this question can be given in terms of relational properties of the vector encoding.…”