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arXiv:1811.02711 · Physical Review A

Resource-efficient analyzer of Bell and Greenberger-Horne-Zeilinger states of multiphoton systems

Tao Li, Adam Miranowicz, Keyu Xia, Franco Nori

Published Nov 1, 2019• 35 citations

Abstract

We propose a resource-efficient error-rejecting entangled-state analyzer for polarization-encoded multiphoton systems. Our analyzer is based on two single-photon quantum-nondemolition detectors, where each of them is implemented with a four-level emitter (e.g., a quantum dot) coupled to a one-dimensional system (such as a micropillar cavity or a photonic nanocrystal waveguide). The analyzer works in a passive way and can completely distinguish ${2}^{n}$ Greenberger-Horne-Zeilinger (GHZ) states of $n$ photons without using any active operation or fast switching. The efficiency and fidelity of the GHZ-state analysis can, in principle, be close to unity, when an ideal single-photon scattering condition is fulfilled. For a nonideal scattering, which typically reduces the fidelity of a GHZ-state analysis, we introduce a passively error-rejecting circuit to enable a near-perfect fidelity at the expense of a slight decrease of its efficiency. Furthermore, the protocol can be directly used to perform a two-photon Bell-state analysis. This passive, resource-efficient, and error-rejecting protocol can, therefore, be useful for practical quantum networks.

DOI: 10.1103/physreva.100.052302

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We propose a resource-efficient error-rejecting entangled-state analyzer for polarization-encoded multiphoton systems. Our analyzer is based on two single-photon quantum-nondemolition detectors, where each of them is implemented with a four-level emitter (e.g., a quantum dot) coupled to a one-dimensional system (such as a micropillar cavity or a photonic nanocrystal waveguide). The analyzer works in a passive way and can completely distinguish

{2}^{n}

Greenberger-Horne-Zeilinger (GHZ) states of

n

photons without using any active operation or fast switching. The efficiency and fidelity of the GHZ-state analysis can, in principle, be close to unity, when an ideal single-photon scattering condition is fulfilled. For a nonideal scattering, which typically reduces the fidelity of a GHZ-state analysis, we introduce a passively error-rejecting circuit to enable a near-perfect fidelity at the expense of a slight decrease of its efficiency. Furthermore, the protocol can be directly used to perform a two-photon Bell-state analysis. This passive, resource-efficient, and error-rejecting protocol can, therefore, be useful for practical quantum networks.

We propose an efficient protocol for complete polarized photons Bell-states and Greenberger–Horne–Zeilinger (GHZ)-states analysis assisted by atoms. With the help of assistant atoms and some simple liner optical elements, the analysis of both polarization Bell states and GHZ states can be performed completely. In our protocol, the assistant atoms are trapped in cavity quantum electronic dynamics (QED), which is feasible with current experimental technology. Moreover, the polarized photons entangled states will not be destroyed in our protocol. Therefore, our scheme might contribute to the quantum communication, quantum computation, and some other fields in quantum information processing.

Photonic graph states are underlying resources for one-way optical quantum computation, quantum error correction, fundamental testing of quantum mechanics, and quantum communication networks. Most existing works, however, are based on the spontaneous parametric down-conversion sources that intrinsically suffer from probabilistic generation and double pair components. Here, we create two important classes of graph states, a polarization-encoded four-photon Greenberger–Horne–Zeilinger (GHZ) state and a linear cluster state, by actively demultiplexing a deterministic single-photon source from a semiconductor quantum dot embedded in a micropillar. A state fidelity of 0.790 ± 0.009 (0.763 ± 0.004) and a count rate of ∼13 Hz are observed for the four-photon GHZ (cluster) state. The results constitute a new route toward the multiphoton entanglement with deterministic single-photon sources.

Hyperentanglement represents a key resource in many quantum information processing schemes. Here, we present a complete and fidelity-robust hyperentangled-Bell-state analysis (HBSA) scheme for two-photon systems entangled in polarization, spatial mode, and time-bin degrees of freedom (DOFs). The scheme uses a fidelity-robust quantum nondemolition (QND) detector called BLOCK1, built with a singly charged semiconductor quantum dot (QD) in a double-sided optical microcavity (double-sided QD-cavity system) under the balance condition, and some linear-optical elements. Compared with the previously proposed complete HBSA schemes based on ideal optical giant circular birefringence, our scheme guarantees the robust fidelity and relaxes the requirement on the QD-cavity parameters with the assistance of the balance condition. Different from the schemes using error-detected blocks and exchanging Bell states in different DOFs to get unity fidelity, the BLOCK1 under the balance condition can directly measure the Bell states of polarization and spatial mode so that fewer kinds of linear optical components are needed in our scheme. In addition, our scheme simplifies the discrimination process and reduces the required light–matter interaction by using a self-assisted mechanism. These features indicate that our scheme may be directly generalized to multiphoton hyperentangled Greenberger–Horne–Zeilinger state analysis and more feasible in practical quantum applications based on the photonic hyperentanglement.

The Bell state plays a significant role in the fundamental tests of quantum mechanics, such as the nonlocality of the quantum world. The Bell-state analysis is of vice importance in quantum communication. Existing Bell-state analysis protocols usually focus on the Bell-state encoding in the physical qubit directly. In this paper, we will describe an alternative approach to realize the near complete logic Bell-state analysis for the polarized concatenated Greenberger-Horne-Zeilinger (C-GHZ) state with two logic qubits. We show that the logic Bell-state can be distinguished in two steps with the help of the parity-check measurement (PCM) constructed by the cross-Kerr nonlinearity. This approach can be also used to distinguish arbitrary C-GHZ state with N logic qubits. As both the recent theoretical and experiment work showed that the C-GHZ state has its robust feature in practical noisy environment, this protocol may be useful in future long-distance quantum communication based on the logic-qubit entanglement.