Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects

TL;DR

This paper introduces an operational scheme linking measurement invasiveness to non-classical memory effects in open quantum systems, providing a new way to identify quantum memory through violations of non-invasive measurability.

Contribution

It develops a theoretical framework connecting measurement invasiveness with quantum memory effects, applicable to various open quantum system dynamics including Lindblad and microscopic models.

Findings

Violation of non-invasive measurability indicates non-classical memory effects.

The approach applies to diverse quantum dynamics, including stochastic and bipartite Lindblad models.

Conditions for Leggett-Garg inequality violation are derived from this perspective.

Abstract

An operational (measurement based) scheme that connects measurement invasiveness and the presence of non-classical memory effects in open quantum systems is defined. Its underlying theoretical basis relies on a non-invasive measurability of (memoryless) quantum Markovian dynamics when the corresponding observable is diagonal in the same basis as the system density matrix. In contrast, violation of this property can be related to intrinsic non-classical memory effects. Related conditions for violation of Leggett-Garg inequality due to quantum memory effects emerge from this perspective. The developed approach applies to open quantum dynamics whose time-evolution is derived from a full unitary (microscopic) description, stochastic Hamiltonian dynamics, as well as for a broad class of non-unitary system-environment models (bipartite Lindblad equations).