Bounds on entanglement in qudit subsystems

Details Bounds on entanglement in qudit subsystems Bounds on entanglement in qudit subsystems

2002-03-07

arxiv.org/abs/quant-ph/0203037v3

Phys. Rev. A 66, 062310 (2002)

Physics

Quantum Physics

7 pages, 3 embedded eps figures. v2 is restructured, one fig replaced, improved explanations, references updated; main results

Scientific paper

10.1103/PhysRevA.66.062310

The entanglement in a pure state of N qudits (d-dimensional distinguishable quantum particles) can be characterised by specifying how entangled its subsystems are. A generally mixed subsystem of m qudits is obtained by tracing over the other N-m qudits. We examine the entanglement in the space of mixed states of m qudits. We show that for a typical pure state of N qudits, its subsystems smaller than N/3 qudits will have a positive partial transpose and hence are separable or bound entangled. Additionally, our numerical results show that the probability of finding entangled subsystems smaller than N/3 falls exponentially in the dimension of the Hilbert space. The bulk of pure state Hilbert space thus consists of highly entangled states with multipartite entanglement encompassing at least a third of the qudits in the pure state.

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