Osittaisjäljellä

Osittaisjäljellä is a Finnish term that translates to "partial trace" in English. It is a concept found in quantum mechanics and quantum information theory, referring to a mathematical operation used to simplify the description of a quantum system when it is entangled with another system. When a quantum system is entangled with another, its state cannot be fully described independently. The partial trace allows one to derive the quantum state of a subsystem without needing to know the complete state of the entire entangled system.

The process involves summing over the degrees of freedom of the unwanted subsystem. Mathematically, if you have a composite system described by a density matrix $\rho_{AB}$ where A and B are two subsystems, the partial trace over subsystem B, denoted as $\text{Tr}_B(\rho_{AB})$, yields the reduced density matrix for subsystem A, $\rho_A$. This operation effectively "averages out" or "traces out" the influence of subsystem B, providing the statistical description of subsystem A as if it were isolated.

The partial trace is a fundamental tool for analyzing entanglement, quantum computation, and quantum thermodynamics. It enables researchers to study the properties of individual parts of a larger quantum system, which is crucial for understanding how quantum information is processed and how quantum states evolve. Without the partial trace, it would be significantly more complex to analyze the behavior of subsystems within entangled states.