Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities

Abstract

Hyperentanglement has attracted much attention due to its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatialpolarization mixed hyperentangled Bell state with the errors in both the spatial-mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. We also propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglement.Entanglement, a unique phenomenon in quantum physics, is an essential resource in quantum information processing, such as quantum computing [1], quantum key distribution [2], quantum secure direct communication [3,4], quantum teleportation [5], quantum dense coding [6,7], quantum secret sharing [8,9], and so on. In long-distance quantum communication, entangled photon pairs always act as a quantum channel and they are usually produced locally and inevitably polluted by the environment noise in the distribution process between the two legitimate users. With current technology, the photon signals can be transmitted no more than several hundreds of kilometers in an optical fiber or a free space, so quantum repeaters are required to connect the two neighboring nodes in a long-distance quantum communication network. Also, the entanglement of photon pairs will decrease in the storage process, which will decrease the fidelity and the security of long-distance quantum communication protocols. In quantum repeaters, entanglement purification and entanglement concentration are two necessary quantum techniques for improving the entanglement of the entangled systems.Entanglement purification is used to obtain highfidelity nonlocal entangled states from mixed states with less entanglement [10][11][12][13][14][15][16][17][18][19]. Up to now, many entanglement purification protocols (EPPs) were proposed for the polarization photon systems, resorting to nonlinear optics [10][11][12][13] or linear optics [14][15][16][17][18][19]. Entanglement concentration is used to obtain the maximally entangled

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

“…Hyperentangled states have also been used to accomplish deterministic entanglement purification of polarization entanglement [22][23][24][25], construct hyperparallel photonic quantum computing [26,27] and quantum repeaters [28]. Entanglement concentration and entanglement purification protocols for hyperentangled state have also been proposed with the aim of establishing maximally hyperentangled channels between distant parties [29][30][31][32][33][34][35][36].…”

Hyperentanglement concentration for time-bin and polarization hyperentangled photons

“…In 2013, Ren, Du, and Deng [49] presented the parameter-splitting method, a very efficient way for entanglement concentration with linear optics, and they gave the first hyperentanglement concentration protocol for two-photon four-qubit systems, which was extended to multipartite entanglement subsequently [50]. Subsequently, Ren and Deng proposed the first hyperentanglement purification protocol and an efficient hyper-ECP assisted by diamond NV centers inside photonic crystal cavities [51]. In 2014, Ren, Du, and Deng gave a two-step hyperentanglement purification protocol for polarizationspatial hyperentangled states with the quantum-statejoining method.…”

Systematic entanglement concentration for unknown less-entangled three-photon W states

“…ment purification [16][17][18][19][20][21] (which works in a completely deterministic way, not in a probabilistic way, and they can reduce the quantum resource sacrificed largely [22]), and entanglement concentration [23][24][25][26][27][28][29][30][31][32][33][34][35][36]. By definition, entanglement purification protocols are used to distill some high-fidelity entangled photon systems from a lessentangled ensemble in a mixed entangled state [12][13][14][15][16][17][18][19][20][21] while entanglement concentration protocols (ECPs) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]…”

“…By definition, entanglement purification protocols are used to distill some high-fidelity entangled photon systems from a lessentangled ensemble in a mixed entangled state [12][13][14][15][16][17][18][19][20][21] while entanglement concentration protocols (ECPs) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] are used to obtain a subset of photon systems in a maximally entangled state from a set of systems in a partially entangled pure state. The former is more general as a photon system is usually in a mixed entangled state after it is transmitted over a noisy channel, but the latter is a more efficient in some particular cases, such as those with decoherence of entanglement arising from the storage process or the imperfect entanglement source.…”