Quantum speed limits and the maximal rate of information production

Abstract

The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present analysis, we derive equivalent statements by relying on only two fundamental results in quantum information theory and quantum dynamics -Fannes inequality and the quantum speed limit. As main results, we obtain Bremermann-Bekenstein-type bounds for the rate of change of the von Neumann entropy in quantum systems undergoing open system dynamics, and for the rate of change of the Shannon information over some logical basis in unitary quantum evolution.

Non-uniform magnetic field as a booster for quantum speed: faster quantum information processing

“…The current study possesses a high outreach potential. It has the scope for applications in burgeoning fields such as, relativistic quantum thermodynamics [38,39], quantum information [40] and quantum metrology [41]. In today's scenario, the role of non-uniform magnetic field is not limited only to the realm of physics but also has a broad perspective.…”

Advances on quantum speed limit

“…研究表明, 在量子热动力学中, 基于量子速度极限 可以获得量子熵产的最大速率 [10] . 基于量子速度极限 对熵产的影响, 人们建立了量子信息最大产率的界 限 [101] . 然而, 这个界限只限于数学上的推导并要求熵 是连续的.…”

Extensions of the Mandelstam-Tamm quantum speed limit to systems in mixed states

“…In this appendix, we derive the formula (18) for the geodesic distance between two projectors P 0 and P 1 in G(n, H) equipped with the metric g g defined in (15).…”