Tradeoff relations in open quantum dynamics via Robertson, Maccone-Pati, and Robertson-Schrödinger uncertainty relations

Abstract

The Heisenberg uncertainty relation, together with Robertson's generalisation, serves as a fundamental concept in quantum mechanics, showing that noncommutative pairs of observables cannot be measured precisely. In this study, we explore the Robertson-type uncertainty relations to demonstrate their effectiveness in establishing a series of thermodynamic uncertainty relations and quantum speed limits in open quantum dynamics. The derivation utilises a scaled continuous matrix product state representation that maps the time evolution of the quantum continuous measurement to the time evolution of the system and field. Specifically, we consider the Maccone-Pati uncertainty relation, a refinement of the Robertson uncertainty relation, to derive thermodynamic uncertainty relations and quantum speed limits. These newly derived relations, which use a state orthogonal to the initial state, yield bounds that are tighter than previously known bounds. Moreover, we consider the Robertson-Schrödinger uncertainty, which extends the Robertson uncertainty relation. Our findings not only reinforce the significance of the Robertson-type uncertainty relations, but also expand its applicability in identifying uncertainty relations in open quantum dynamics.

arXiv comment22 pages, 1 figure, 1 table

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Cited by in corpus (3)

• Speed limits and thermodynamic uncertainty relations for quantum systems governed by non-Hermitian Hamiltonian
• Thermodynamic concentration inequalities and tradeoff relations
• Thermodynamic entropic uncertainty relation