Two Qubits for C.G. Jung's Theory of Personality
Reinhard Blutner, Elena Hochnadel
Abstract:
We propose a formalization of C.G. Jung's theory of personality using
a four-dimensional Hilbert-space for the representation of two
qubits. The first qubit relates to Jung's four psychological functions
Thinking, Feeling, Sensing and iNtuition, which are represented by two
groups of projection operators {T, F} and {S, N}. The operators in
each group are commuting but operators of different groups are
not. The second qubit represents Jung's two perspectives of
extraversion and introversion. It is shown that this system gives a
natural explanation of the 16 psychological types that are defined in
the Jungian tradition. Further, the system accounts for the
restriction posed by Jung concerning the possible combination of
psychological functions and perspectives. Interestingly, the unitary
transformation called X-gate in the quantum computation community
realizes the cognitive operation connected to Jung's idea of the
shadow. The empirical consequences of the present model are discussed
and it is shown why the present praxis of personality diagnostics
based on classical statistics is insufficient.