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Scientific Reports

Implementation of SWAP test for two unknown states in photons via cross-Kerr nonlinearities under decoherence effect

Min-Sung Kang, Jino Heo, Seong Gon Choi, Sung Moon, Sang-Wook Han

Published Apr 16, 2019• 32 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-019-42662-4

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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.
We propose an arbitrary controlled-unitary (CU) gate and a bidirectional transfer scheme of quantum information (BTQI) for unknown photons. The proposed CU gate utilizes quantum non-demolition photon-number-resolving measurement based on the weak cross-Kerr nonlinearities (XKNLs) and two quantum bus beams; the proposed CU gate consists of consecutive operations of a controlled-path gate and a gathering-path gate. It is almost deterministic and is feasible with current technology when a strong amplitude of the coherent state and weak XKNLs are employed. Compared with the existing optical multi-qubit or controlled gates, which utilize XKNLs and homodyne detectors, the proposed CU gate can increase experimental realization feasibility and enhance robustness against decoherence. According to the CU gate, we present a BTQI scheme in which the two unknown states of photons between two parties (Alice and Bob) are mutually swapped by transferring only a single photon. Consequently, by using the proposed CU gate, it is possible to experimentally implement the BTQI scheme with a certain probability of success.
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.
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.
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.
Quantum phase estimation (QPE) is the key procedure in various quantum algorithms. The main aim of the QPE scheme is to estimate the phase of an unknown eigenvalue, corresponding to an eigenstate of an arbitrary unitary operation. The QPE scheme can be applied as a subroutine to design many quantum algorithms. In this paper, we propose the basic structure of a QPE scheme that could be applied in quantum algorithms, with feasibility by utilizing cross-Kerr nonlinearities (controlled-unitary gates) and linearly optical devices. Subsequently, we analyze the efficiency and the performance of the controlled-unitary gate. This gate consists of a controlled-path gate and a merging-path gate via cross-Kerr nonlinearities under the decoherence effect. Also shown in this paper is a method by which to enhance robustness against the decoherence effect to provide a reliable QPE scheme based on controlled-unitary gates.