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arXiv:1601.03755 · Laser Physics Letters

Hyperconcentration for multipartite entanglement via linear optics

Xihan Li, Shohini Ghose

Published Oct 22, 2014• 51 citations
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Abstract

We present a hyperconcentration scheme for nonlocal N -photon hyperentangled Greenberger–Horne–Zeilinger states. The maximally hyperentangled state, in which N particles are entangled simultaneously in the polarization and the spatial mode, can be obtained with a certain probability from two partially hyperentangled states. The hyperconcentration scheme is based on one polarization parity check measurement, one spatial mode parity check measurement and N − 2 single-photon two-qubit measurements. The concentration only requires linear optical elements, which makes it feasible and practical with current technology.

DOI
10.1088/1612-2011/11/12/125201

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We present a hyperconcentration scheme for nonlocal N -photon hyperentangled Greenberger–Horne–Zeilinger states. The maximally hyperentangled state, in which N particles are entangled simultaneously in the polarization and the spatial mode, can be obtained with a certain probability from two partially hyperentangled states. The hyperconcentration scheme is based on one polarization parity check measurement, one spatial mode parity check measurement and N − 2 single-photon two-qubit measurements. The concentration only requires linear optical elements, which makes it feasible and practical with current technology.
We propose two schemes for concentration of hyperentanglement of nonlocal multipartite states which are simultaneously entangled in the polarization and spatial modes. One scheme uses an auxiliary single-photon state prepared according to the parameters of the less-entangled states. The other scheme uses two less-entangled states with unknown parameters to distill the maximal hyperentanglement. The procrustean concentration is realized by two parity check measurements in both the two degrees of freedom. Nondestructive quantum nondemolition detectors based on cross-Kerr nonlinearity are used to implement the parity check, which makes the unsuccessful instances reusable in the next concentration round. The success probabilities in both schemes can be made to approach unity by iteration. Moreover, in both schemes only one of the N parties has to perform the parity check measurements. Our schemes are efficient and useful for quantum information processing involving hyperentanglement.
Hyperentanglement has attracted considerable attention recently because of its high-capacity for long-distance quantum communication. In this study, we present a hyperentanglement concentration protocol (hyper-ECP) for nonlocal three-photon systems in the polarization, spatial-mode, and time-bin partially hyperentangled Greenberger–Horne–Zeilinger (GHZ) states using the Schmidt projection method. In our hyper-ECP, the three distant parties must perform the parity-check measurements on the polarization, spatial-mode, and time-bin degrees of freedom, respectively, using linear optical elements and Pockels cells, and only two identical nonlocal photon systems are required. This hyper-ECP can be directly extended to the N -photon hyperentangled GHZ states, and the success probability of this general hyper-ECP for a nonlocal N -photon system is the optimal one, regardless of the photon number N .
We present two hyperconcentration protocols for hyperentangled states, in which entanglement occurs simultaneously in the polarization and the spatial degrees of freedom. One uses an auxiliary single photon prepared in a fixed state. The other uses two less-entangled photon pairs. In both schemes, a two photon maximally hyperentangled state can be obtained from the nonmaximally entangled states with a certain success probability. The procrustean concentration is realized by polarizing beam splitters and nondestructive quantum nondemolition detection. In both protocols the unsuccessful instances can be reconcentrated repeatedly to get a higher success probability, which makes our schemes efficient and useful in quantum information processing.
We propose an efficient hyperconcentration protocol for distilling maximally hyperentangled state from partially entangled pure state, resorting to the projection measurement on an auxiliary photon. In our scheme, two photons simultaneously entangled in polarization states and spatial modes are considered. One party performs quantum nondemolition detections on his photon and an additional photon to produce three photon hyperentangled state, then he projects the assistant photon into an orthogonal basis composed of both the polarization and spatial degree of freedom. Then the state of the left two photons collapses into maximally hyperentangled state with a certain probability. In the rest cases, some less-entangled states are obtained, which can be used as resource for the next round concentration. By repeating the concentration process for several rounds, a higher success probability can be obtained, which makes our scheme useful in practical quantum information applications.
We present two hyperentanglement concentration schemes for two-photon states that are partially entangled in the polarization and time-bin degrees of freedom. The first scheme distills a maximally hyperentangled state from two identical less-entangled states with unknown parameters via the Schmidt projection method. The other scheme can be used to concentrate an initial state with known parameters and requires only one copy of the initial state for the concentration process. Both these two protocols can be generalized to concentrate NNN-photon hyperentangled Greenberger-Horne-Zeilinger states that are simultaneously entangled in the polarization and time-bin degrees of freedom. Our schemes require only linear optics and are feasible with current technology. Using the time-bin degree of freedom rather than the spatial-mode degree of freedom can provide savings in quantum resources, which makes our schemes practical and useful for long-distance quantum communication.
We present two hyperentangled concentration schemes for two-photon systems in a partially hyperentangled Bell state that is simultaneously entangled in polarization, spatial mode and time-bin degrees of freedom (DOFs). The first scheme extracts a maximally hyperentangled Bell state using cross-Kerr nonlinearity, which is discussed in two cases of unknown and known coefficients. We construct quantum nondemolition detectors based on cross-Kerr nonlinearities to implement the polarization and spatial parity check. In this scheme, we only require a small phase shift, as long as it can be distinguished from zero. The second scheme is used to concentrate an initial partially hyperentangled state with only linear optical elements, where coefficients of the initial state are known. Both of the two schemes are feasible with the current experimental technology. Moreover, hyperentanglement DOFs can largely improve the channel capacity of long-distance quantum communication. All of these make our schemes more practical and useful in quantum communication.