Bounds on entanglement in qudit subsystems

Kendon, Vivien ; Zyczkowski, Karol ; Munro, William

HP Development Company

关键词: quantum information;    coherent pulses;    quantum gate;   

RP-ID  :  HPL-2002-124

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

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 this mixed space 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. Notes: Vivien Kendon, Optics Section, Blackett Laboratory, Imperial College, London SW7 2BW UK Karol Zyczkowski, Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotnikow 32/44, 02- 668 Warszawa, Poland 7 Pages