Emergent non-Markovianity and dynamical quantification of the quantum switch

TL;DR

This paper explores how the quantum switch induces a form of quantum memory, leading to non-Markovian dynamics, and introduces measures to quantify this switch-induced memory and its effects on quantum information loss.

Contribution

It reveals that the quantum switch causes emergent non-Markovianity and proposes a measure to quantify switch-induced quantum memory, advancing understanding of quantum memory effects.

Findings

Quantum switch induces a specific form of quantum memory.

Switch action leads to non-Markovian dynamics.

Derived an uncertainty relation between information loss and memory.

Abstract

We investigate the dynamical aspects of the quantum switch and find a particular form of quantum memory emerging out of the switch action. We first analyze the loss of information in a general quantum evolution subjected to a quantum switch and propose a measure to quantify the switch-induced memory. We then derive an uncertainty relation between information loss and switch-induced memory. We explicitly consider the example of depolarizing dynamics and show how it is affected by the action of a quantum switch. For a more detailed analysis, we consider both the control qubit and the final measurement on the control qubit as noisy and investigate the said uncertainty relation. Further, while deriving the Lindblad-type dynamics for the reduced operation of the switch action, we identify that the switch-induced memory actually leads to the emergence of non-Markovianity. Interestingly, we demonstrate that the emergent non-Markovianity can be explicitly attributed to the switch operation by comparing it with other standard measures of non-Markovianity. Our investigation thus paves the way forward to understanding the quantum switch as an emerging non-Markovian quantum memory.