# Is there any reasonable dynamics for quantum subsystems within the unitary-only quantum theory?

## TL;DR

This paper investigates the dynamics of quantum subsystems within unitary-only quantum theory, proving non-existence of trajectories for certain Markovian processes and discussing implications for quantum measurement and interpretation.

## Contribution

It provides a no-go theorem showing the non-existence of subsystem trajectories in Hilbert space for specific Markovian processes, challenging the viability of purely unitary dynamics.

## Key findings

- Proves non-existence of trajectories in Hilbert space for some Markovian processes
- Suggests mixed states can be dynamically associated with single subsystems
- Demonstrates the impossibility of defining quantum histories in these models

## Abstract

The foundational studies of the standard, unitary-only quantum theory revolve around the kinematical aspects of quantum entanglement and the improper quantum mixtures. In this paper, we introduce and argue for the foundational character of the question of dynamics of quantum subsystems (open quantum systems). In this context, for some typical and physically relevant Markovian processes, we technically prove non-existence of trajectories in the Hilbert state space of the open system. As a kind of no-go theorem for the unitary-only quantum theory, this finding suggests that the mixed quantum states may be joined to the individual (single) quantum subsystem dynamically described by the corresponding master equation. Then the problem of interpretation of improper mixtures dissolves while description of quantum measurement boils down to the problem of reduction of the mixed to the pure states-i.e. to the problem of actualization of definite values of certain observables of the single open systems, thus tackling the mathematical problem of interpreting probability for the single trials of an experiment. This kind of indeterminism may be the furthest we can go within the dynamical approach to quantum subsystems. As an alternative appears the possibility that the idea of dynamics of quantum subsystems may not be viable in the context of the unitary-only theory. As a direct consequence of our main finding appears the a priori impossibility to define "quantum history" in the Hilbert state space for the considered Markovian models.