Unitality Conditions on Subsystems in Quantum Dynamics

TL;DR

This paper establishes a fundamental link between the unitality of noise acting on a quantum system and its environment, revealing how this relationship influences the evolution and quantum correlations in composite quantum states.

Contribution

It demonstrates that unital (non-unital) noise on a system requires the environment to also be unital (non-unital) for the joint evolution to be unitary, clarifying noise effects in quantum dynamics.

Findings

Unital noise on the system implies unital noise on the environment for unitary evolution.

Non-unital noise on the system implies non-unital noise on the environment for unitary evolution.

Different quantum states (GHZ vs. W) exhibit distinct unitality behaviors in their joint evolution.

Abstract

It is known that non-unital noise such as the amplitude damping can sometimes increase quantum correlations, while unital noise such as the dephasing usually decreases quantum correlations. It is, therefore, important to delineate the conditions, when noise can enhance the quantumness of the system. Here, we show that if the noise acting on the system is unital (non-unital), then the noise acting on the environment must also be unital (non-unital), for the evolution to be unitary in the joint system-environment space. For example, if the first two qubits are treated as system and the third qubit is treated as environment, then both the system and the environment evolve unitally in case of a three-qubit GHZ state, and both of them evolve non-unitally in case of a three-qubit W state. Our result may be of interest in quantum information, and we anticipate it to be useful in various contexts, such as to better tackle noise in quantum computing and quantum information processing.