Initial-state-dependent thermalization in open qubits

TL;DR

This paper investigates how a qubit's equilibrium state, influenced by initial conditions and environment interactions, can be described thermodynamically using an entanglement Hamiltonian and temperature, with geometric insights and validation via quantum walk.

Contribution

It introduces a thermodynamic framework for initial-state-dependent thermalization in open qubits, highlighting the role of entanglement Hamiltonian and temperature in describing equilibrium states.

Findings

Thermal states can be characterized by an entanglement Hamiltonian.

Initial state influences the entanglement temperature.

Results confirmed through quantum walk simulations.

Abstract

We study, from a thermodynamic perspective, the equilibrium states of a qubit interacting with an arbitrary environment of dimension N>>2. We show that even in presence of memory about the initial state, in some cases the qubit can be considered in a thermal state characterized by an entanglement Hamiltonian, which encodes the effects of the environment, and an initial-state- dependent entanglement temperature that measures the degree of entanglement generated between the system and its environment. Geometrical aspects of the thermal states are studied, and the results are confirmed for the concrete case of the Quantum Walk on the Line.