0000000000803774
AUTHOR
Giulia Gualdi
A tomographic approach to non-Markovian master equations
We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function of some unknown time-independent parameters, we show that these parameters can be reconstructed by means of a finite number of tomograms. Two different approaches towards reconstruction, integral and differential, are presented and applied to a benchmark model made of a harmonic oscillator coupled to a bosonic bath. For this model the number of tomograms needed to retrieve the unknown parameters is explicitly computed.
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identifi…
Reconstruction of time-dependent coefficients: a check of approximation schemes for non-Markovian convolutionless dissipative generators
We propose a procedure to fully reconstruct the time-dependent coefficients of convolutionless non-Markovian dissipative generators via a finite number of experimental measurements. By combining a tomography based approach with a proper data sampling, our proposal allows to relate the time-dependent coefficients governing the dissipative evolution of a quantum system to experimentally accessible quantities. The proposed scheme not only provides a way to retrieve full information about potentially unknown dissipative coefficients but also, most valuably, can be employed as a reliable consistency test for the approximations involved in the theoretical derivation of a given non-Markovian convo…
Reconstruction of Markovian master equation parameters through symplectic tomography
In open quantum systems, phenomenological master equations with unknown parameters are often introduced. Here we propose a time-independent procedure based on quantum tomography to reconstruct the potentially unknown parameters of a wide class of Markovian master equations. According to our scheme, the system under investigation is initially prepared in a Gaussian state. At an arbitrary time t, in order to retrieve the unknown coefficients one needs to measure only a finite number (ten at maximum) of points along three time-independent tomograms. Due to the limited amount of measurements required, we expect our proposal to be especially suitable for experimental implementations.