18-Qubit Entanglement with Six Photons' Three Degrees of Freedom

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18-Qubit Entanglement with Six Photons’ Three Degrees of Freedom

Xi-Lin Wang, Yi-Han Luo, He-Liang Huang, Ming-Cheng Chen, Zu-En Su, Chang Liu, Chao Chen, Wei Li, Yu-Qiang Fang, Xiao Jiang, Jun Zhang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan

Phys. Rev. Lett. 120, 260502 – Published 28 June 2018

Abstract

Full control of multiple degrees of freedom of multiple particles represents a fundamental ability for quantum information processing. We experimentally demonstrate an 18-qubit Greenberger-Horne-Zeilinger entanglement by simultaneous exploiting three different degrees of freedom of six photons, including their paths, polarization, and orbital angular momentum. We develop high-stability interferometers for reversible quantum logic operations between the photons’ different degrees of freedom with precision and efficiencies close to unity, enabling simultaneous readout of $2^{18} = 262 144$ outcome combinations of the 18-qubit state. A state fidelity of $0.7 08 \pm 0.0 16$ is measured, confirming the genuine entanglement of all 18 qubits.

Received 19 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.120.260502

Physics Subject Headings (PhySH)

Angular momentum of light Entanglement production Nonlocality Optical quantum information processing Quantum computation Quantum optics

Quantum Information, Science & Technology

Authors & Affiliations

Xi-Lin Wang, Yi-Han Luo, He-Liang Huang, Ming-Cheng Chen, Zu-En Su, Chang Liu, Chao Chen, Wei Li, Yu-Qiang Fang, Xiao Jiang, Jun Zhang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan

Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; CAS Centre for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; and CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China

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Vol. 120, Iss. 26 — 29 June 2018

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Images

Figure 1
Scheme and experimental setup for creating and verifying the 18-qubit GHZ state consisting of six photons and 3 d.o.f. (a) The generation of the six-photon polarization-entangled GHZ state. An ultrafast laser with a central wavelength of 788 nm, a pulse duration of 140 fs, and a repetition rate of 80 MHz is focused on a lithium triborate (LBO) and up-converted to 394 nm. The ultraviolet laser is focused on three custom-designed sandwichlike nonlinear crystals, each consists of two 2-mm-thick $β$ -barium borates (BBOs) and one HWP to produce three pairs of entangled photons. In each output, two pieces of ${YVO}_{4}$ crystals with different thickness and orientation are used for spatial and temporal compensation for the birefringence effects. The three pairs of entangled photons are combined on two PBSs to generate a six-photon polarization-entangled GHZ state. (b) For each single photon, it is sent through a double PBS, and two SPPs to be prepared in a single-photon three-qubit state. (c) The measurement of the spatial qubit with closed (dash line) or open (without the dash line) interferometric configuration. (d) Polarization measurement. (e) High-efficiency and dual-channel OAM readout by coherently convert the OAM to polarization by a swap gate (inset). (f) Photo of the actual setup used in (b) and (c). By vertical translation, it is convenient to switch between open and closed (g). Real-time monitoring of the visibilities in the spatial (f) and OAM (h) measurements. (h) Photo of the actual setup used in (e). DP: Dove prism.
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Figure 2
Experimental data of 18-qubit GHZ entanglement. The (a) $N = 1$ , (b) $N = 3$ , (c) $N = 12$ , and (d) $N = 18$ qubits are measured in the superposition base $(| 0 ⟩ \pm e^{i θ} | 1 ⟩) / \sqrt{2}$ . Each of the $N$ -qubit events corresponds to the observation of an eigenstate of the observable $M_{θ}^{\otimes N} = {(\cos θ σ_{x} + \sin θ σ_{y})}^{\otimes N}$ with an eigenvalue of $v_{s} = + 1$ or $v_{s} = - 1$ . The expectation values $⟨ M_{θ}^{\otimes N} ⟩$ can be calculated by $⟨ M_{θ}^{\otimes N} ⟩ = \sum_{s = 1}^{2^{N}} p_{s} v_{s}$ , where $p_{s} (s = 1, ..., 2^{N})$ is the relative probability of the $N$ -qubit detection events. The $x$ axis denotes the phase shift $θ$ between $| 0 ⟩$ and $| 1 ⟩$ , and the $y$ axis is the experimentally obtained $⟨ M_{θ}^{\otimes N} ⟩$ . Error bars indicate 1 standard deviation and are calculated by the experimentally detected $N$ -qubit events with the propagated Poissonian counting statistics. In (a)–(c), the error bars are smaller than the data points. (e) 18-qubit events in the computational $| 0 ⟩ / | 1 ⟩$ basis accumulated for 2 h are displayed in a $512 \times 512 = 262 144$ dimensional matrix.
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