# Conditional past-future correlation induced by non-Markovian dephasing reservoirs

## TL;DR

This paper investigates quantum non-Markovianity through conditional past-future correlations in a qubit system, revealing memory effects induced by non-Markovian dephasing reservoirs and their relation to measurement back action.

## Contribution

It provides exact solutions for a qubit coupled to various dephasing environments and links memory effects to measurement back action even under time-independent Lindblad dynamics.

## Key findings

- Memory effects can develop without time-dependent Lindblad equations.
- Lorentzian distributed parameters induce non-Markovian behavior.
- Measurement back action influences system dynamics between measurements.

## Abstract

Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as for classically fluctuating random Hamiltonian models. The developing of memory effects and departures from Born-Markov or white-noise approximations are related to a measurement back action that changes the system dynamics between consecutive measurements. It is shown that this effect may develop even when the former system evolution is given by a time-independent Lindblad equation. This unusual non-Markovian case arises when the characteristic parameters of the dynamics become Lorentzian random distributed variables.