We consider the bilinear Schroedinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global approximate controllability.

Perturbation theory of eigenvalue problems

Controllability of bilinear quantum systems in explicit times via explicit control fields

We consider here the problem of controlling a parameter-dependent family of quantum systems by a single vector-valued control law. We do so by exploiting adiabatic approximation and conically connected spectra for the controlled Hamiltonian. For three-level stimulated Raman adiabatic passage (STIRAP) we recover the celebrated counterintuitive solution.

Additional excerpts

Ensemble control of parameter-dependent quantum systems by adiabatic evolution

In this work, a biharmonic elliptic system is investigated in $\mathbb{R}^{N}$
 , which involves singular potentials and multiple critical exponents. By the Rellich inequality and the symmetric criticality principle, the existence and multiplicity of G-invariant solutions to the system are established. To our best knowledge, our results are new even in the scalar cases.

/pdf/on-g-invariant-solutions-of-a-singular-biharmonic-elliptic-5c9odcdv63.pdf

On G-invariant solutions of a singular biharmonic elliptic system involving multiple critical exponents in R N $R^{N}$

background

Centre de math ematiques appliqu ees

Abstract Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive. 

/pdf/detecting-positive-quantum-capacities-of-quantum-channels-sni5j31o.pdf

Perturbation theory of eigenvalue problems

Citations

Controllability of bilinear quantum systems in explicit times via explicit control fields

Ensemble control of parameter-dependent quantum systems by adiabatic evolution

On G-invariant solutions of a singular biharmonic elliptic system involving multiple critical exponents in R N $R^{N}$

Centre de math ematiques appliqu ees

Detecting positive quantum capacities of quantum channels

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