Hyperentanglement concentration for two-photon four-qubit systems with linear optics

Abstract

Hyperentanglement, defined as the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention recently. Here we investigate the possibility of concentrating the two-photon four-qubit systems in partially hyperentangled states in both the spatial mode and the polarization DOFs with linear optics. We first introduce our parameter-splitting method to concentrate the systems in the partially hyperentangled states with known parameters, including partially hyperentangled Bell states and cluster states. Subsequently, we present another two nonlocal hyperentanglement concentration protocols (hyper-ECPs) for the systems in partially hyperentangled unknown states, resorting to the Schmidt projection method. It will be shown that our parameter-splitting method is very efficient for the concentration of the quantum systems in partially entangled states with known parameters, resorting to linear-optical elements only. All these four hyper-ECPs are feasible with current technology and they may be useful in long-distance quantum communication based on hyperentanglement as they require only linear optical elements.

Efficient entanglement concentration for partially entangled cluster states with weak cross-Kerr nonlinearity

“…Furthermore, this protocol does not require sophisticated single-photon detector as the QND has the function of a photon number detector. Actually, it should be noted that the linear optical elements in the current ECPs are common in current experiment conditions, such as PBSs, HWP 45 s, and conventional photon detectors, which have been widely used in ECPs [54,55], but not ideal. For the success probability to our calculation, we assume the efficiency of the linear optical elements is perfect.…”

Hyperentanglement purification with linear optics assisted by W-states

“…It has been shown in previous works that hyperentanglement concentration [31] and hyperdistillation [32] can be performed using linear optics. A nonlinear optics-based protocol is also reported for hyperentanglement purification in both polarization and spatial-mode DOFs with a fidelity of 95.7 % assisted by NV centers inside photonic crystal cavities [30].…”

Efficient single-photon-assisted entanglement concentration for an arbitrary entangled photon pair with the diamond nitrogen-vacancy center insides cavity

“…To overcome this flaw, one can exploit entanglement purification [11][12][13][14][15][16][17] or entanglement concentration [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]40] to improve the entanglement of the quantum system first, and then achieve the goals of the above applications with the maximally entangled states. The methods of converting an ensemble of less-entangled mixed state into a maximally entangled state is called entanglement purification [11][12][13][14][15][16][17].…”