Quantum Jarzynski Equality with multiple measurement and feedback for isolated system
arXiv:1111.6229 · doi:10.1007/s12043-012-0304-7
Abstract
In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast to the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.
7 pages
References in corpus (7)
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Information heat engine: converting information to energy by feedback control
- Second Law of Thermodynamics with Discrete Quantum Feedback Control
- Quantum Feedback Control of Atomic Motion in an Optical Cavity
- Fluctuation theorems for continuously monitored quantum fluxes
- Quantum Jarzynski-Sagawa-Ueda relations
- Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control
Cited by in corpus (8)
- Extracting work from a single heat bath - A case study on Brownian particle under external magnetic field in presence of information
- Nonequilibrium work and entropy production by quantum projective measurements
- Derivation of the not-so-common fluctuation theorems
- Verifying detailed fluctuation relations for discrete feedback-controlled quantum dynamics
- Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum
- Universal interpretation of efficacy parameter in perturbed nonequilibrium systems
- Extended Fluctuation Theorems for Repeated Measurements and Feedback within Hamiltonian Framework
- Heat exchange and fluctuation in Gaussian thermal states in the quantum realm