Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement

Abstract

We present a complete hyperentangled Bell state analysis protocol for two-photon four-qubit states which are simultaneously entangled in the polarization and time-bin degrees of freedom. The 16 hyperentangled states can be unambiguously distinguished via two steps. In the first step, the polarization entangled state is distinguished deterministically and nondestructively with the help of the cross-Kerr nonlinearity. Then, in the second step, the time-bin state is analyzed with the aid of the polarization entanglement. We also discuss the applications of our protocol for quantum information processing. Compared with hyperentanglement in polarization and spatial-mode degrees of freedom, the polarization and time-bin hyperentangled states provide saving in quantum resources since there is no requirement for two spatial modes for each photon. This is the first complete hyperentangled Bell state analysis scheme for polarization and time-bin hyperentangled states, and it can provide new avenues for high-capacity, long-distance quantum communication.

High-dimensional one-way quantum processing implemented on d-level cluster states

“…Hyper-entanglement within energy-time entangled states. Hyper-entangled states are quantum states which are entangled in two or more independent degrees of freedom 23,26,36,43 , such as polarization, optical paths, or orbital angular momentum. Since these degrees of freedom can be controlled autonomously, such systems can be best described as multi-partite states, where each degree of freedom represents an independent party 23,36 .…”

Quantum hyperentanglement and its applications in quantum information processing

“…In quantum communication, hyperentanglement can be used to increase the channel capacity largely, besides its application for assisting the implementation of quantum communication protocols based on one DOF. HBSA is the prerequisite for quantum communication protocols with hyperentanglement, and it is one of the important parts in high-capacity quantum repeaters [36][37][38][39][40][41][42][43][44][45]. We have reviewed the high-capacity long-distance quantum communication protocols based on polarization-spatial hyperentanglement, including the complete HBSA scheme with the cross-Kerr nonlinearity, the quantum teleportation of a quantum state in both the polarization and the spatial-mode DOFs with polarization-spatial hyperentanglement, and the hyperentanglement swapping of polarization-spatial hyperentangled Bell states.…”

“…Li and Ghose [41] presented a very simple scheme for the self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity and another interesting HBSA scheme [42] for polarization and time-bin hyperentanglement. Up to now, there are several important schemes for the analysis of hyperentangled states [36][37][38][39][40][41][42][43][44][45], including the probabilistic one based on linear optical elements [44] and the one for hyperentangled Greenberger-Horne-Zeilinger (GHZ) states [45]. In 2015, Wang et al [66] demonstrated in experiment the quantum teleportation of an unknown quantum state of a single photon in multiple DOFs by implementing the HBSA of two-photon systems probabilistically with linear optical elements and ancillary entanglement sources.…”

“…In the applications of hyperentanglement, the complete hyperentangled-Bell-state analysis (HBSA) [36][37][38][39][40][41][42][43][44][45], hyper-teleportation of quantum state with more than one DOF [36], hyperentanglement swapping [37], hyperentanglement concentration [46][47][48][49][50][51][52][53], hyperentanglement purification [47,[54][55][56][57], and universal entangling quantum gates for hyperparallel photonic quantum computation [58][59][60][61][62] are very useful and important. HBSA is the prerequisite for high-capacity quantum communication protocols with hyperentanglement and it is used to distinguish the hyperentangled states.…”

Remote preparation for single-photon state in two degrees of freedom with hyper-entangled states

“…These DoFs can be used to construct hyper-entanglement, which refer to the entangled in multiple DoFs of a quantum system simultaneously. Recently, hyper-entanglement becomes a promising quantum resource due to its high capacity of channel, and it has extensive applications in quantum information processing, such as Bell-state analysis with hyper-entanglement [38][39][40][41][42][43][44], quantum repeaters [45], entanglement swapping [42,46,47], hype-entanglement concentration [48,49], and so on. So far, experimental progress of hyper-entanglement generation has been reported using different photonic DoFs [50][51][52][53][54][55][56][57][58].…”