Quantum mechanics

Statistics

Markov process

Markov chain

Computer science

Observable

Statistical physics

Relation (database)

Quantum system

Software

Physics

Database

Mathematics

Political science

Unitary state

Quantum

Programming language

Open system (computing)

Open quantum system

Physical Review Letters

We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in the environment by the survival activity, which reduces to the dynamical activity in classical Markov processes. Remarkably, the relation derived herein holds for general open quantum systems with any counting observable and any initial state. Therefore, our relation is satisfied for classical Markov processes with arbitrary time-dependent transition rates and initial states. We apply our relation to continuous measurement and the quantum walk to find that the quantum nature of the system can enhance the precision. Moreover, we can make the lower bound arbitrarily small by employing appropriate continuous measurement.

Thermodynamic Uncertainty Relation for General Open Quantum Systems