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Progress of Theoretical and Experimental Physics

Splitting and acquiring quantum information with perfect $W$ states based on weak cross-Kerr nonlinearities

Xiao‐Ming Xiu, Cen Cui, Yan-Fang Lin, Li Dong, Haikuan Dong, Yajun Gao

Published Nov 20, 2017• 5 citations
Publisher

Abstract

With the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media, we propose a scheme to split and acquire quantum information with three-photon perfect W states.By means of a fault-tolerant circuit, the perfect W states are distributed to the participants without being affected by the collective noise.And on this basis we present a scheme for splitting and acquiring a single-photon state with the shared perfect W states. Together with the mature techniques of classical feed-forward, simple and available linear optical elements are applied in the procedure, enhancing the feasibility of the theoretical scheme proposed here.........

DOI
10.1093/ptep/ptx173

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Splitting and acquiring quantum information with perfect WWW states based on weak cross-Kerr nonlinearities
With the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media, we propose a scheme to split and acquire quantum information with three-photon perfect W states.By means of a fault-tolerant circuit, the perfect W states are distributed to the participants without being affected by the collective noise.And on this basis we present a scheme for splitting and acquiring a single-photon state with the shared perfect W states. Together with the mature techniques of classical feed-forward, simple and available linear optical elements are applied in the procedure, enhancing the feasibility of the theoretical scheme proposed here.........
Relying on weak cross-Kerr nonlinearities, we propose a nearly deterministic generation scheme of the three-photon polarization-entangled perfect WWW state which can be applied to the perfect teleportation of an unknown single-photon state and has robust entanglement against the loss of one photon of them. Three photons entangle together by virtue of the bus function of the coherent state serving as the intermediate among them. In the scheme, three processes are executed successively and two kinds of modules are inserted into the circuit, where the homodyne measurement and the photon number measurement are aptly performed. By means of classical feedforward techniques, single-photon unitary transformation operations are performed on the corresponding photons based on the obtained measurement outcomes, by which the generation efficiency of the perfect WWW state aims to nearly unity. Moreover, some currently available optical elements are applied in the generation process, which offer facilities for the practical implementation.
We propose a three-party scheme for quantum information splitting (QIS) of an arbitrary single-photon polarization state based on weak cross-Kerr nonlinearity combined with linear optics elements such as polarization beam splitters (PBSs) and half wave plates (HWPs). The scheme is generalized to the arbitrary-party case. With the help of quantum nondemolition (QND) measurements, our schemes can be accomplished in an almost deterministic way. The two schemes are feasible with the current technology.
Based on the circuit including linear optical elements, a fault-tolerant distribution of GHZ states against collective noise among three parties is proposed. Additionally, two controlled DSQC protocols using the shared GHZ states as quantum channels are also presented under the charge of the controller. The first controlled DSQC protocol applies single parity analysis based on weak cross-Kerr nonlinearities. The receiver Bob performs single-photon measurement to obtain the secret information after the outcome publication of the single parity analysis executed by the sender Alice. The second protocol applies dense coding to double information transmission capacity, and the double parity analyses based on weak cross-Kerr nonlinearities are performed to obtain the secret information.
We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B28, 2030 (2011)]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.
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.
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.