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Minimising heat dissipation of bit erasure by controlling a finite-size quantum reservoir

Mohammady, M. ; Mohseni, M. ; Omar, Y.

Minimising heat dissipation of bit erasure by controlling a finite-size quantum reservoir, Proc Workshop on , Belfast, United Kingdom, Vol. N/A, pp. N/A - N/A, August, 2014.

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Abstract
We determine the optimal unitary evolution on a composite system composed of a qubit,
the object to be erased, and a thermal reservoir of dimension d < , so as to minimise the
heat dissipation to the reservoir conditional on maximally reducing the entropy of the qubit:
of maximally erasing its information. We consider the simple example of erasing a maximally
mixed qubit using a reservoir with a uniform energy gap between consecutive eigenstates, such
as a harmonic oscillator. We show that in the limit as both d and Hamiltonian norm tend to
infinity the heat dissipation due to a log(2) reduction in entropy obeys the inequality Q 1,
with the equality reached in the limit of the energy spectrum forming a continuum. We also
show that in the presence of pure dephasing bit erasure can be made more efficient by both
increasing the dimension of the reservoir and decreasing the energy gap. Furthermore, we
provide a scheme for decreasing heat dissipation by using an auxiliary system in addition to
the thermal reservoir. We conclude by showing that if the qubit is a subsystem of a thermal
reservoir, heat dissipation due to maximal bit erasure is minimised when the qubit is initially
uncorrelated with the other subsystems of the reservoir.