A Computational Model for Quantum Measurement
Received March 3, 2003; accepted August 13, 2003
Is the dynamical evolution of physical systems objectively a manifestation of
information processing by the universe? We ﬁnd that an afﬁrmative answer has
important consequences for the measurement problem. In particular, we calculate
the amount of quantum information processing involved in the evolution of physical
systems, assuming a ﬁnite degree of ﬁne-graining of Hilbert space. This assumption
is shown to imply that there is a ﬁnite capacity to sustain the immense entanglement
that measurement entails. When this capacity is overwhelmed, the system’s unitary
evolution becomes computationally unstable and the system suffers an information
transition (‘‘collapse’’). Classical behavior arises from the rapid cycles of unitary
evolution and information transition. Thus, the ﬁne-graining of Hilbert space
determines the location of the ‘‘Heisenberg cut’’, the mesoscopic threshold
separating the microscopic, quantum system from the macroscopic, classical
environment. The model can be viewed as a probablistic complement to decoherence,
that completes the measurement process by turning decohered improper mixtures of
states into proper mixtures. It is shown to provide a natural resolution to the
measurement problem and the basis problem.
KEY WORDS: Quantum measurement theory; quantum information
processing; entanglement production.
PACS: 03.65.Ta; 03.67.-a; 03.67.Lx; 03.67.Mn.
Inspite of the tremendous success of standard quantum mechanics, its
interpretational aspects continue to puzzle us, particularly in regard to
measurement and its extrapolation to the macroscopic level.
overwhelming number of current studies and applications of quantum
mechanics do not depend on the philosophical resolutions of these difﬁculties,
they will become important for understanding future experiments where
advancing technology will permit one to probe mesoscopic phenomena.
Raman Research Institute, Bangalore-560 080, Karnataka, India. E-mail: firstname.lastname@example.org
Quantum Information Processing, Vol. 2, No. 3, June 2003 (# 2003)
1570-0755/03/0600–0153/0 # 2003 Plenum Publishing Corporation