A successive approximation method for quantum separability

doi:10.1007/s11464-013-0274-1

Front Math Chin

2013, Vol. 8

Issue (6) : 1275-1293 https://doi.org/10.1007/s11464-013-0274-1

RESEARCH ARTICLE

A successive approximation method for quantum separability

Deren HAN¹(

), Liqun QI²

1. School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China; 2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

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Abstract

Determining whether a quantum state is separable or inseparable (entangled) is a problem of fundamental importance in quantum science and has attracted much attention since its first recognition by Einstein, Podolsky and Rosen [Phys. Rev., 1935, 47: 777] and Schr?odinger [Naturwissenschaften, 1935, 23: 807-812, 823-828, 844-849]. In this paper, we propose a successive approximation method (SAM) for this problem, which approximates a given quantum state by a so-called separable state: if the given states is separable, this method finds its rank-one components and the associated weights; otherwise, this method finds the distance between the given state to the set of separable states, which gives information about the degree of entanglement in the system. The key task per iteration is to find a feasible descent direction, which is equivalent to finding the largest M-eigenvalue of a fourth-order tensor. We give a direct method for this problem when the dimension of the tensor is 2 and a heuristic cross-hill method for cases of high dimension. Some numerical results and experiences are presented.

Keywords Quantum system entanglement tensor successive approximation M-eigenvalue cross-hill

Corresponding Author(s): HAN Deren,Email:handeren@njnu.edu.cn

Issue Date: 01 December 2013

Cite this article:

Deren HAN,Liqun QI. A successive approximation method for quantum separability[J]. Front Math Chin, 2013, 8(6): 1275-1293.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-013-0274-1
https://academic.hep.com.cn/fmc/EN/Y2013/V8/I6/1275

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