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Register a new userLinear Quantum Entropy and Non-Hermitian Hamiltonians
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We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.
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We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find that one needs both the normalized and non-normalized density operators in order to properly describe irreversible processes. It turns out that such a generalization monitors the onset of disorder in quantum dissipative systems. We give arguments for why one can consider the generalized entropy as the informational entropy describing the flow of information between the system and the bath. We illustrate the theory by explicitly studying few simple models, including tunneling systems with two energy levels and non-Hermitian detuning.
We report on a time scaling technique to enhance the performances of quantum protocols in non-Hermitian systems. The considered time scaling involves no extra-couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum state transfers in 2 and 3-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that, with an appropriate driving, the time-scaling technique preserves the optimality of the quantum speed with respect to the quantum speed limit while reducing significantly the damping of the quantum state norm.
In this work we address systems described by time-dependent non-Hermitian Hamiltonians under time-dependent Dyson maps. We shown that when starting from a given time-dependent non-Hermitian Hamiltonian which is not itself an observable, an infinite chain of gauge linked time-dependent non-observable non-Hermitian Hamiltonians can be derived from it. The matrix elements of the observables associated with all these non observable Hamiltonians are, however, all linked to each other, and in the particular case where global gauges exist, these matrix elements becomes all identical to each other. In this case, therefore, by approaching whatever the Hamiltonian in the chain we can get information about any other Hamiltonian. We then show that the whole chain of time-dependent non-Hermitian Hamiltonians collapses to a single time-dependent non-Hermitian Hamiltonian when, under particular choices for the time-dependent Dyson maps, the observability of the Hamiltonians is assured. This collapse thus shows that the observability character of a non-Hermitian Hamiltonian prevents the construction of the gauge-linked Hamiltonian chain and, consequently, the possibility of approaching one Hamiltonian from another.
The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decays. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.
For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and the lines bundle L^n over M such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of L^n. We examine the case of 2 x 2 matrix Hamiltonians in detail and show that, contrary to claims made in some recent publications, geometric phases arising from encircling exceptional points are generally geometrical and not topological in nature.
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