The theory establishes that for open quantum systems interacting with an unobserved environment (modelled by Bob), a local observer's predictions regarding expectation values and measurement statistics on their subsystem (A) are fully described not by state rays in Hilbert space but by the density operator $\rho_A$, defined via partial trace over the environmental degrees of freedom. The formal framework defines quantum states as Hermitian, non-negative operators with unit trace ($\text{Tr}(\rho)=1$), allowing for a unified mathematical description of pure states and statistical ensembles arising from decoherence or lack of complete information regarding correlations (entanglement). This concept belongs to the domain of Open Quantum Systems theory, serving as the foundational formalism for analyzing non-unitary dynamics, mixed states, and entanglement properties within the broader discipline of quantum mechanics.
The theory establishes that for open quantum systems interacting with an unobserved environment (modelled by Bob), a local observer's predictions regarding expectation values and measurement statisti…