A random quantum state of three qubits is not always entangled

Zhi Li of National Research Council Canada and Perimeter Institute for Theoretical Physics, along with colleagues, demonstrate that a tripartite Haar random state cannot always be distilled into bipartite entanglement using standard local operations. The work establishes that when each of three subsystems, A, B, or C, holds fewer than half of the total qubits, no EPR-like entanglement can be extracted. Specifically, the researchers derive an upper bound on the probability of finding such entanglement, revealing a decrease as the number of qubits increases. This finding challenges a previous belief within the AdS/CFT correspondence that a necessarily implies bipartite entanglement. Haar random states involving three qubits cannot reliably produce bipartite entanglement through local operations, a result that challenges expectations for random quantum systems. This absence…