Geometry of local quantum dissipation and fundamental limits to local cooling

TL;DR

This paper geometrically characterizes one-qubit Lindblad dissipators, revealing fundamental limits to local cooling and maximum achievable entanglement, with implications for quantum thermodynamics.

Contribution

It introduces an efficient parametrization of one-qubit dissipators and analyzes the fundamental quantum limits to local cooling and entanglement.

Findings

Maximum steady-state singlet fraction is approximately 0.654.

Discontinuity in singlet fraction at the transition from unital to non-unital dissipators.

Fundamental quantum limit prevents cooling below a certain non-zero temperature.

Abstract

We geometrically characterize one-qubit dissipators of a Lindblad type. An efficient parametrization in terms of 6 linear parameters opens the way to various optimizations with local dissipation. As an example, we study maximal steady-state singlet fraction that can be achieved with an arbitrary local dissipation and two qubit Hamiltonian. We show that this singlet fraction has a discontinuity as one moves from unital to non-unital dissipators and demonstrate that the largest possible singlet fraction is approximately 0.654. This means that for systems with a sufficiently entangled ground state there is a fundamental quantum limit to the lowest attainable energy. With local dissipation one is unable to cool the system below some limiting non-zero temperature.