Possible approach to solving the phase problem of coherence theory

Demosthenes Dialetis, E. Wolf

Alexander Streltsov, Swapan Rana, Paul Boës +1 more

Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between the classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations that arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization for incoherent operations, constituted by all possible transformations allowed within the resource theory of coherence. In this Letter, we contribute to such a characterization by proving several upper bounds on the maximum number of incoherent Kraus operators in a general incoherent operation. For a single qubit, we show that the number of incoherent Kraus operators is not more than 5, and it remains an open question if this number can be reduced to 4. The presented results are also relevant for quantum thermodynamics, as we demonstrate by introducing the class of Gibbs-preserving strictly incoherent operations, and solving the corresponding mixed-state conversion problem for a single qubit.

Emmanouil George Thrapsaniotis

In the present paper, we calculate the sign solved propagator of a two electrons two dimensional (2D) atom by solving the sign problem. We apply the sign solved propagator expression to the evaluation of the geometric phase of the ground state of the 2D helium atom that is derived variationally. 2D quantum dots are another possible area of application of the present theory.

Jan Peřina

Soma, Gaius

Valentin S. Idiatulin

A study is made of the excitation of inhomogeneous holographic gratings by ultrashort light pulses with an arbitrary amplitude and phase modulation in a cubic nonlinear medium. The relaxation and diffusion of a pulse-induced grating is considered. The problem of diffraction of probe radiation by an inhomogeneous grating is solved using an electrodynamic theory of perturbations and also using the coupled wave approximation. It is shown that a cubic nonlinear medium may be used to store and then to retrieve uniquely a complete complex coherence function of a pulse. A simple method is proposed for the determination of the area under an exciting pulse, which makes it possible to introduce integral parameters of such a pulse (including a generalized amplitude and duration) that can serve as satisfactory estimates of the corresponding real quantities.