# Environment¶

*The references that inspired this chapter are all mentioned in the*
References
*section*.

## Quantum channels¶

Quantum channels, also known as quantum maps [B2] or quantum operations [B3], are a mean to describe the three different kinds of evolution that may affect an open quantum system:

Unitary evolution obeying the dynamics prescribed by the closed system’s Hamiltonian

Measurement

Erratic interaction with the environment (noise)

Keywords:

Density operator, the key representation of the state of open systems

- Quantum maps, Kraus sum representation /Quantum operations, operator-sum representation

More to investigate:

*Tensor networks and graphical calculus for open quantum systems*[136],in relation with the*Pauli Transfer Matrix (PTM) representation of a Quantum Channel*(see PTM on qiskit), and*completely positive trace preserving (CPTP) maps*

## Master equation¶

The Lindblad master equation.

A differential equation that formalizes the evolution of the system under the action of its environment. The involved \(L_\mu\) operators describe the relaxation events which affect the system, and can be, in many cases, guessed from a careful analysis of the system.

The evolution according to the master equation can be numerically evaluated by Monte Carlo simulations.