Detection of the ideal resource for multiqubit teleportation

Zhao, Ming‐Jing; Chen, Bin; Fei, Shao-Ming

doi:10.1088/1674-1056/24/7/070302

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…[1,2] It has wide applications in quantum information processing. [3][4][5][6][7][8][9][10][11][12] The separability problem, namely distinguishing separable states from entangled states, is a challenging task whose complexity scales very unfavorably with the size of the system. [13] A possible approach is to consider sufficient criteria for entanglement.…”

Section: Introductionmentioning

confidence: 99%

Detecting high-dimensional multipartite entanglement via some classes of measurements

Liu¹,

Gao²,

Yan³

2018

Chinese Phys. B

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Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the k-nonseparability (k is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of m subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography. PACS numbers: 03.67.Mn, 03.65.Ud I. INTRODUCTIONQuantum entanglement is one of the most intriguing features of quantum mechanics which lies at the heart of quantum information sciences [1,2]. It has wide applications in diverse fields ranging from condensed matter [3] to high-energy field theory [4]. The separability problem, namely distinguishing separable states from entangled states, is a challenging task whose complexity scales very unfavorably with the size of the system [5]. A possible approach is to consider sufficient criteria for entanglement. For bipartite systems, various separability criteria have been proposed.When it comes to multipartite systems, the situation becomes much more complicated, because there exhibits much richer structure than bipartite case [5]. Although the detection of multipartite entangled states is a harder challenge, it is worthy of study because they have advantages when performing some tasks [6]. Many attempts have been made to frame multipartite entanglement detection, such as witnessing genuine multipartite entanglement [7-9], detecting k-nonseparable states [10-13], etc. The main challenge for high-dimensional multipartite systems is not only to develop mathematical tools for entanglement detection, but also to find schemes whose experimental implementation requires minimal effort, that is to say, we need to detect entanglement with as few measurements as possible, specifically independent of full state tomography.The notion of mutually unbiased bases (MUBs) was first introduced under a different name [14]. Many quantum information protocols depend upon the use of MUBs [15], such as quantum key distribution, the reconstruction of quantum states, etc. The concept of MUBs was generalized to mutually unbiased measurements (MUMs) [16] due to the open problem of the maximum number of MUBs for non-prime power dimensions which limits its applications [17]. The construction of a complete set of d + 1 MUMs were found [16] in a finite, d-dimensional Hilbert space, no matter whether d is a prime power. Symmetric informationally complete positive operator-valued measures (SIC-POVMs) is another related topic in quantum information, which has many helpful connections with MUBs, such as operational link [18]...

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