Typical entanglement in multi-qubit systems

Details Typical entanglement in multi-qubit systems Typical entanglement in multi-qubit systems

2001-06-05

arxiv.org/abs/quant-ph/0106023v2

J. Mod. Optics, 49 (10), 1709-1716, 2002

Physics

Quantum Physics

4 pages, 5 embedded eps figures, RevTeX4, minor revisions, to appear in J. Mod. Optics

Scientific paper

10.1080/09500340110120914

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's 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 PPT (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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