Positive and non-positive measurements in energy extraction from quantum batteries
arxiv(2024)
摘要
We extend the concept of stochastic energy extraction from quantum batteries
to the scenario where both positive operator-valued (POV) and physically
realizable non-positive operator-valued measurements are applied (NPOVMs) on
the auxiliary connected to the battery in presence of noise. The process
involves joint evolution of the battery and the auxiliary for a particular time
interval, an interaction of the auxiliary with its environment which induces
noise in the auxiliary, and performing a POVM or NPOVM on the auxiliary, and
finally the selection of a particular measurement outcome. Application of POVM
on the auxiliary can be realised by attaching an external system to the
auxiliary, which is initially in a product state with the rest of the system,
and performing a joint projective measurement on the auxiliary and external. On
the other hand, if there are interactions leading to correlations among the
auxiliary, environment, and external systems, then performing the projective
measurement on the auxiliary-environment-external system can be interpreted as
a physically realizable NPOVM operation on the auxiliary. We however utilize
interaction between the auxiliary and the environment to implement NPOVMs on
the auxiliary. We find the expressions of stochastically extractable energy by
performing POVMs and NPOVMs on the auxiliary and show that the latter does not
depend on the applied noise. Focusing on a particular model of the governing
Hamiltonian of a qubit battery and an auxiliary, and considering the presence
of amplitude damping noise affecting the auxiliary, we show that stochastically
extractable energy using NPOVMs is no less than that using POVMs. This
advantage of using NPOVMs remains also for bit-flip noise. For dephasing noise,
the energies by applying POVMs and NPOVMs are the same. We additionally
consider the case when a limited set of measurement operators are allowed.
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