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# Bringing quantum jumps under control

Held by Prof. Howard M.
Wiseman (Griffith University, Brisbane, Australia)

Joint work with
Dr. Raisa I. Karasik (Griffith University, Brisbane, Australia)

Abstract:

The modern understanding of quantum jumps is that it
is the dynamics resulting from the typical form of evolution equation
for the conditional state of an open quantum system – the typical
form of a stochastic quantum filtering equation to use control theory
language. If the average (unconditioned) system evolution is ergodic
and Markovian then an experimenter can, in principle, monitor the bath
to which the system is coupled with sufﬁcient precision to make the
conditioned system state pure in the long-time limit. In general, the
quantum jumps, plus the between-jump evolution, create a trajectory
which passes through inﬁnitely many different pure states. That is,
it would take, in principle, an infinite classical memory to keep
track of the state of the quantum system. Here we show that we can use
control to realize an adaptive monitoring scheme on the bath which
brings this infinity under control. Specifically, for any finite
dimensional system, one can expect to ﬁnd an adaptive monitoring
that conﬁnes the system state to jumping between only finitely many
states [1]. That is, the adaptive tracking scheme can be realized as a
finite-state machine. We show specifically for a two-level system how
such a scheme can be constructed and analyse its stability [2].

[1] R. Karasik and H. M. Wiseman, “How many bits does it take to
track an open quantum system?”, Phys. Rev. Lett. 106, 020406 (2011).

[2] R. Karasik and H. M. Wiseman, “Tracking an open quantum
system using a ﬁnite state machine: stability analysis”,
arXiv:1106.4292