Probing entanglement of a continuous basis system

In this paper, we propose a method to probe entanglement in a theoretically inaccessible quantum system with either a discrete or continuous basis. Our approach leverages insights into the entanglement distribution within a four-partite quantum system, comprising two qubit-oscillator subsystems with dephasing interactions between each qubit-oscillator pair. The method involves measurements applied only to the accessible two-qubit subsystem, enabling a qualitative detection and characterization of quantum correlations in the inaccessible two-oscillator subsystem. This approach provides a novel framework for probing entanglement in continuous-basis systems where traditional measures are often inapplicable due to their complexity. Our findings also reveal an intriguing conservative flow-like behavior in the redistribution of entanglement among subsystems, suggesting that entanglement may exhibit conservative properties in pure composite quantum systems.