Qubit control using quantum Zeno effect: Action principle approach
arXiv:2211.08773 · doi:10.1016/j.aop.2023.169222
Abstract
We employ the stochastic path-integral formalism and action principle for continuous quantum measurements - the Chantasri-Dressel-Jordan (CDJ) action formalism [1, 2] - to understand the stages in which quantum Zeno effect helps control the states of a simple quantum system. The detailed dynamics of a driven two-level system subjected to repeated measurements unravels a myriad of phases, so to say. When the detection frequency is smaller than the Rabi frequency, the oscillations slow down, eventually coming to a halt at an interesting resonance when measurements are spaced exactly by the time of transition between the two states. On the other hand, in the limit of large number of repeated measurements, the dynamics organizes itself in a rather interesting way about two hyperbolic points in phase space whose stable and unstable directions are reversed. Thus, the phase space flow occurs from one hyperbolic point to another, in different ways organized around the separatrices. We believe that the systematic treatment presented here paves the way for a better and clearer understanding of quantum Zeno effect in the context of quantum error correction.
References in corpus (15)
- A Straightforward Introduction to Continuous Quantum Measurement
- To catch and reverse a quantum jump mid-flight
- Quantum Zeno effect by general measurements
- Measurement quantum mechanics and experiments on quantum Zeno effect
- Action principle for continuous quantum measurement
- Determining the Quantum Expectation Value by Measuring a Single Photon
- Stochastic path integral formalism for continuous quantum measurement
- Quantum Zeno effect appears in stages
- Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission
- Quantum Zeno Effect with the Feynman-Mensky Path-Integral Approach
- Quantum Zeno and Anti-Zeno probes of noise correlations in photon polarisation
- Prediction and Characterization of Multiple Extremal Paths in Continuously Monitored Qubits
- Pitfalls of Path Integrals: Amplitudes for Spacetime Regions and the Quantum Zeno Effect
- The information about the state of a charge qubit gained by a weakly coupled quantum point contact
- Resonances and adiabatic invariance in classical and quantum scattering theory