Typical entanglement in multiple-qubit systems

Kendon, Vivien and Nemoto, Kae and Munro, William (2002) Typical entanglement in multiple-qubit systems. Journal of Modern Optics, 49 (10). pp. 1709-1716. ISSN 0950-0340 (https://doi.org/10.1080/09500340110120914)

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Abstract

Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is reasonably well understood; however, the nature and properties of multiple qubit systems are largely unexplored. Motivated by the importance of such systems in quantum computing, we show that typical pure states of N qubits are highly entangled but have decreasing amounts of pairwise entanglement (measured using the Wootter concurrence formula) as N increases. Above six qubits, very few states have any pairwise entanglement and, generally, for a typical pure state of N qubits there is a sharp cut-off where its subsystems of size m become positive partial transpose (i.e. separable or only bound entangled) around N ≳ 2m + 3, based on numerical analysis up to N = 13.

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