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Scientific Reports

Distribution of hybrid entanglement and hyperentanglement with time-bin for secure quantum channel under noise via weak cross-Kerr nonlinearity

Jino Heo, Min-Sung Kang, Changho Hong, Hyung-Jin Yang, Seong Gon Choi, Jong-Phil Hong

Published Aug 25, 2017• 13 citations
Publisher

Abstract

We design schemes to generate and distribute hybrid entanglement and hyperentanglement correlated with degrees of freedom (polarization and time-bin) via weak cross-Kerr nonlinearities (XKNLs) and linear optical devices (including time-bin encoders). In our scheme, the multi-photon gates (which consist of XKNLs, quantum bus [qubus] beams, and photon-number-resolving [PNR] measurement) with time-bin encoders can generate hyperentanglement or hybrid entanglement. And we can also purify the entangled state (polarization) of two photons using only linear optical devices and time-bin encoders under a noisy (bit-flip) channel. Subsequently, through local operations (using a multi-photon gate via XKNLs) and classical communications, it is possible to generate a four-qubit hybrid entangled state (polarization and time-bin). Finally, we discuss how the multi-photon gate using XKNLs, qubus beams, and PNR measurement can be reliably performed under the decoherence effect.

DOI
10.1038/s41598-017-09510-9

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Europhysics Letters (EPL)•Oct 22, 2018•30 citations
We design schemes to generate and distribute hybrid entanglement and hyperentanglement correlated with degrees of freedom (polarization and time-bin) via weak cross-Kerr nonlinearities (XKNLs) and linear optical devices (including time-bin encoders). In our scheme, the multi-photon gates (which consist of XKNLs, quantum bus [qubus] beams, and photon-number-resolving [PNR] measurement) with time-bin encoders can generate hyperentanglement or hybrid entanglement. And we can also purify the entangled state (polarization) of two photons using only linear optical devices and time-bin encoders under a noisy (bit-flip) channel. Subsequently, through local operations (using a multi-photon gate via XKNLs) and classical communications, it is possible to generate a four-qubit hybrid entangled state (polarization and time-bin). Finally, we discuss how the multi-photon gate using XKNLs, qubus beams, and PNR measurement can be reliably performed under the decoherence effect.
We design an optical scheme to generate hyperentanglement correlated with degrees of freedom (DOFs) via quantum dots (QDs), weak cross-Kerr nonlinearities (XKNLs), and linearly optical apparatuses (including time-bin encoders). For generating hyperentanglement having its own correlations for two DOFs (polarization and time-bin) on two photons, we employ the effects of optical nonlinearities using a QD (photon-electron), a parity gate (XKNLs), and time-bin encodings (linear optics). In our scheme, the first nonlinear multi-qubit gate utilizes the interactions between photons and an electron of QD confined in a single-sided cavity, and the parity gate (second gate) uses weak XKNLs, quantum bus, and photon-number-resolving measurement to entangle the polarizations of two photons. Finally, for efficiency in generating hyperentanglement and for the experimental implementation of this scheme, we discuss how the QD-cavity system can be performed reliably, and also discuss analysis of the immunity of the parity gate (XKNLs) against the decoherence effect.
Abstract Herein, we present a scheme to prepare a hybrid-entangled W state that possesses the polarization states of two photons and the time-bin using cross-Kerr nonlinearities (XKNLs) and linearly optical devices. To maximize the merit of the entangled W state that can conserve entanglement against the loss of one qubit, we propose a method to prepare a two-photon hybrid-entangled W state correlated with degrees of freedom (polarization and the time-bin) via nonlinearly optical gates using XKNLs. In our scheme, the nonlinear gates consist of weak XKNLs, quantum bus beams, and photon-number-resolving measurements to realize the controlled-path gate and merging-path gate between two photons. To insert the time-bin information into photons, the time-bin encoder employs only linearly optical devices (delay lines and polarizing beam splitters). Subsequently, to evaluate the efficiency and experimental feasibility of our scheme for generating a two-photon hybrid-entangled W state, we analyzed the performance of nonlinear gates using XKNLs under the decoherence effect.
We present a scheme to encode quantum information (single logical qubit information) into three-photon decoherence-free states, which can conserve quantum information from collective decoherence, via nonlinearly optical gates (using cross-Kerr nonlinearities: XKNLs) and linearly optical devices. For the preparation of the decoherence-free state, the nonlinearly optical gates (multi-photon gates) consist of weak XKNLs, quantum bus (qubus) beams, and photon-number-resolving (PNR) measurement. Then, by using a linearly optical device, quantum information can be encoded on three-photon decoherence-free state prepared. Subsequently, by our analysis, we show that the nonlinearly optical gates using XKNLs, qubus beams, and PNR measurement are robust against the decoherence effect (photon loss and dephasing) in optical fibers. Consequently, our scheme can be experimentally implemented to efficiently generate three-photon decoherence-free state encoded quantum information, in practice.
Abstract We propose photonic schemes for the distribution and reconstruction of a two-qubit entangled state using a hybrid entangled state under a noisy quantum channel. First, to generate a hybrid entangled state correlated with polarizations and time-bins, we employ a quantum dot (QD)-cavity system (nonlinear optical gate) and linear optical devices to implement controlled operation. These schemes can achieve the distribution and reconstruction of a two-qubit entangled state from hybrid entanglement by utilizing only linear optical devices without a QD-cavity system (i.e., a nonlinear optical device) for users who want to share an entangled state under a noisy quantum channel. For a feasible realization of the proposed schemes, we analyze the interaction between the photons and QD-cavity system and demonstrate the experimental conditions under which the reliable performance of the QD-cavity system is achieved.
We represent an optical scheme using cross-Kerr nonlinearities (XKNLs) and quantum dot (QD) within a single-sided optical cavity (QD-cavity system) to generate three-photon entangled W state containing entanglement against loss of one photon of them. To generate W state (three-photon) with robust entanglement against loss of one photon, we utilize effects of optical nonlinearities in XKNLs (as quantum controlled operations) and QD-cavity system (as a parity operation) with linearly optical devices. In our scheme, the nonlinear (XKNL) gate consists of weak XKNLs, quantum bus beams, and photon-number-resolving measurement to realize controlled-unitary gate between two photons while another nonlinear (QD) gate employs interactions of photons and an electron of QD confined within a single-sided optical cavity for implementation of parity gate. Subsequently, for the efficiency and experimental feasibility of our scheme generating W state, we analyze the immunity of the controlled-unitary gate using XKNLs against decoherence effect and reliable performance of parity gate using QD-cavity system.
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.