Distinguishing limit of Bell states for any $n$-photon $D$-dimensional hyperentanglement

• URL: http://arxiv.org/abs/2011.13251v1
• Date: Thu, 26 Nov 2020 11:43:44 GMT
• Title: Distinguishing limit of Bell states for any $n$-photon $D$-dimensional hyperentanglement
• Authors: Chunzhen Li, Yi Li, Yongnan Li
• Abstract summary: Bell state measurement is crucial to quantum information protocols. It is impossible to unambiguously distinguish all the Bell states encoded in multi-photon using only linear optics.
• Score: 4.446626375802735
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bell state measurement is crucial to quantum information protocols, but it is impossible to unambiguously distinguish all the Bell states encoded in multi-photon using only linear optics. There is a maximum number of distinguished Bell states, i.e. distinguising limit which is very important for increasing the channel capacity of quantum communications. In this paper, we separate $n$-photon $D$-dimensional hyperentanglement into two groups. For the first group of $U$ ($G_1$), we obtain the limit ${N_1} = nD - (n - 1)$, which can be applied for both bosons' and fermions' cases. We further discuss the limit $N$ for any $nD$ system with the second group of $U$ ($G_2$), inferring that at least ${D^{n - 1}}$ Bell states can be distinguished due to the symmetry of Bell states. Obviously, ${N_1} \le {N_2}$ for those systems with $n>2$. Finally, we theoretically design an optical setup for Bell state measurement of two-photon eight-dimensional hyperentanglement of spin, path and orbital angular momentum (OAM) and distinguish 15 classes of 64 Bell states. Our results provide a theoretical basis and practical reference to increase the channel capacity of the quantum communication.

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