Entanglement timescale and mixedness in non-Hermitian quantum systems
- URL: http://arxiv.org/abs/2209.11667v1
- Date: Fri, 23 Sep 2022 15:53:07 GMT
- Title: Entanglement timescale and mixedness in non-Hermitian quantum systems
- Authors: Diego Paiva Pires, Tommaso Macr\`i
- Abstract summary: We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems.
We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states.
Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $mathcalPT$-symmetric quantum field theory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We discuss the short-time perturbative expansion of the linear entropy for
finite-dimensional quantum systems whose dynamics can be effectively described
by a non-Hermitian Hamiltonian. We derive a timescale for the degree of
mixedness for an input state undergoing non-Hermitian dynamics and specialize
these results in the case of a driven-dissipative two-level system. Next, we
derive a timescale for the growth of entanglement for bipartite quantum systems
that depends on the effective non-Hermitian Hamiltonian. In the Hermitian
limit, this result recovers the perturbative expansion for coherence loss in
Hermitian systems, while it provides an entanglement timescale for initial pure
and uncorrelated states. To illustrate these findings, we consider the
many-body transverse-field XY Hamiltonian coupled to an imaginary all-to-all
Ising model. We find that the non-Hermitian Hamiltonian enhances the short-time
dynamics of the linear entropy for the considered input states. Overall, each
timescale depends on minimal ingredients such as the probe state and the
non-Hermitian Hamiltonian of the system, and its evaluation requires low
computational cost. Our results find applications to non-Hermitian quantum
sensing, quantum thermodynamics of non-Hermitian systems, and
$\mathcal{PT}$-symmetric quantum field theory.
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