In quantum mechanics, mixed states are indeed real and play a fundamental role in describing the behavior of quantum systems, including macroscopic objects. A mixed state arises when a quantum system is not in a pure state, meaning it cannot be described by a single wavefunction.
In the case of a macroscopic object, such as your friend in the other room, it is subject to interactions with its environment, which can lead to a process called decoherence. Decoherence occurs when a system interacts with its surroundings, causing the quantum coherence of its wavefunction to break down and behave more classically. As a result, macroscopic objects typically appear to be in a mixed state.
When a macroscopic object is not observed or measured, it can be described by a mixed state, which is a statistical combination of different possible pure states. Each pure state within the mixed state represents a potential outcome if the system were to be measured. These different pure states have associated probabilities, and upon measurement, the system "collapses" into one of the possible outcomes.
The reason why macroscopic objects tend to exhibit classical behavior and are described by mixed states is primarily due to the large number of particles involved and the pervasive interactions with the environment. These interactions result in rapid and complex entanglement between the system and its surroundings, leading to the loss of quantum coherence and the emergence of classical behavior at the macroscopic scale.
It's important to note that the precise boundary between quantum and classical behavior is still an area of active research and debate in the field of quantum mechanics. Different interpretations and approaches exist to address this issue, such as the field of quantum foundations and studies on the emergence of classicality from quantum systems.