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Scientific Reports

Procedure via cross-Kerr nonlinearities for encoding single logical qubit information onto four-photon decoherence-free states

Jino Heo, Seong Gon Choi

Published May 17, 2021• 4 citations
Publisher

Abstract

We propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against the decoherence effect.

DOI
10.1038/s41598-021-89809-w

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We propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against 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 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 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 a scheme for encoding single logical qubit information, which is immune to collective decoherence acting on Hilbert space spanned by the corresponding states. The scheme needs a spatial entanglement gate and a polarization entanglement gate, which are realized with the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media. Under the condition of sufficient large phase shifts, single logical qubit information can be encoded into this minimal optical decoherence-free subsystem with near-unity fidelity. Together with the mature techniques of measurement and classical feed forward, simple linear optical elements are applied to complete the encoding task, which offers the feasibility of this scheme for protecting quantum information against decoherence.
With the assistance of weak cross-Kerr nonlinearities, we present a preparation scheme of four-photon polarization-entangled decoherence-free states, which can be used to construct the minimal optical decoherence-free subspaces where a logical qubit is fully protected against collective decoherence. To complete the preparation task, one spatial entanglement process, two polarization entanglement processes, and one detecting process are applied. The fulfillments of the above processes are contributed by a cross-Kerr nonlinear interaction between the signal photons and a coherent state via Kerr media. Exploiting the available single-photon resource and simple linear optics elements, this scheme is feasible and desirable to be extended to the construction of multiphoton decoherence-free states against the collective decoherence.
We present an optical scheme for a SWAP test (controlled swap operation) that can determine whether the difference between two unknown states (photons) using cross-Kerr nonlinearities (XKNLs). The SWAP test, based on quantum fingerprinting, has been widely applied to various quantum information processing (QIP) schemes. Thus, for a reliable QIP scheme, it is important to implement a scheme for a SWAP test that is experimentally feasible. Here, we utilize linearly and nonlinearly optical (XKNLs) gates to design a scheme for a SWAP test. We also analyze the efficiency and the performance of nonlinearly optical gates in our scheme under the decoherence effect and exhibit a technique employing quantum bus beams and photon-number-resolving measurements to reduce the effect of photon loss and dephasing caused by the decoherence effect. Consequently, our scheme, which is designed using linearly optical devices and XKNLs (nonlinear optics), can feasibly operate the nearly deterministic SWAP test with high efficiency, in practice.