
tary operational postulates – a task which is com-
pleted in the companion paper [
1]. While neither
this question nor the fact that one can recon-
struct quantum theory from elementary axioms is
new and has been extensively explored before in
various contexts [
14–25], we shall approach both
from a novel constructive perspective and with
a stronger emphasis on the conceptual content
of the theory. The ultimate goal of this work is
therefore very rudimentary: to redo a well estab-
lished theory – albeit in a novel way which is es-
pecially engineered for exposing its informational
and logical structure, physical content and dis-
tinctive phenomena more clearly. In other words,
we shall attempt to rebuild quantum theory for
qubit systems from scratch.
In such an information based context it is nat-
ural to follow an operational approach, describing
physics from the perspective of an observer. Ac-
cordingly, we shall work under the premise that
we may only speak about the information an ob-
server has access to in an experiment. Our ap-
proach will thus be purely operational and epis-
temic (i.e. knowledge based) by construction and
shall survive without ontic statements (i.e. ref-
erences to ‘reality’). We shall thus say nothing
about whether or not ‘hidden variables’ could give
rise to the experiences of the observer. Under
these circumstances we adopt an ‘inside view of
physics’, holding properties of systems as being
relationally, rather than absolutely defined.
Indeed, more generally the replacement of ab-
solute by relational concepts goes in hand with
the establishment of universal (i.e. observer in-
dependent) limits. For instance, the crucial step
from Galilean to special relativity is the realiza-
tion that the speed of light c constitutes a univer-
sal limit for information communication among
observers. The fact that all observers agree on
this limit is the origin of the relativity of space
and time. Similarly, the crucial step from classi-
cal to quantum mechanics is the recognition that
the Planck constant ~ establishes a universal limit
on how much simultaneous information is acces-
sible to an observer. While less explicit than in
the case of special relativity, this simple observa-
tion suggests a relational character of a system’s
quantum properties. More precisely, the process
of information acquisition through measurement
establishes an informational relation between the
observer and system. Only if there was no limit
on the acquisition of information would it make
sense to speak about an absolute state of a sys-
tem within a purely operational approach (unless
one accepts the existence of an omniscient and
absolute observer as an external standard). But
thanks to the existence of complementarity, im-
plied by ~, an observer may not access all conceiv-
able properties of the system at once. Further-
more, the observer can choose the experimental
setting and thereby which property of the system
she would like to reveal (although, clearly, she
cannot choose the experimental outcome). Under
our purely operational premise, we shall treat the
situation as if the system does not have any other
properties than those accessible to the observer at
any moment of time. In particular, the system’s
state is naturally interpreted as representing the
observer’s state of information about the system.
These ideas are in agreement with earlier propos-
als in the literature [
26,27] and, most specifically,
with the relational interpretation of qu antum me-
chanics [28 , 29].
Of course, in order for different observers who
may communicate (by physical interaction) to
have a basis for agreeing on the description of
a system, some of its attributes must be observer
independent such as its state space, the set of
possible measurements on it and possibly a limit
on its information content. But without adhering
to an external standard against which measure-
ment outcomes and states could be defined, it is
as meaningless to assert a sy stem’s physical state
to be independent of its relations to other sys-
tems as it is to relate a system’s dynamics to an
absolute Newtonian background time.
It is worthwhile to investigate what we can
learn about physics from such an operational
and informational approach. For this endeavour
we shall adopt the general conviction, which has
been voiced in many different (even conflicting)
ways before in the literature [
26, 28, 30–41], that
quantum theory is best understood as an opera-
tional framework governing an observer’s acquisi-
tion of information about a system. While most
earlier works take quantum theory as given and
attempt to characterize and interpret its physical
content with an emphasis on information infer-
ence, here and in [
1] we take a step back and show
that one can actually derive quantum theory from
this perspective. This will require a focus on the
informational relation between an observer and a
Accepted in Quantum 2017-11-27, click title to verify 2