Efficient Measurement of Multiparticle Entanglement with Embedding Quantum Simulator

Ming-Cheng Chen, Dian Wu, Zu-En Su, Xin-Dong Cai, Xi-Lin Wang, Tao Yang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan

Phys. Rev. Lett. 116, 070502 – Published 18 February 2016

Abstract

The quantum measurement of entanglement is a demanding task in the field of quantum information. Here, we report the direct and scalable measurement of multiparticle entanglement with embedding photonic quantum simulators. In this embedding framework [R. Di Candia et al. Phys. Rev. Lett. 111, 240502 (2013)], the $N$ -qubit entanglement, which does not associate with a physical observable directly, can be efficiently measured with only two (for even $N$ ) and six (for odd $N$ ) local measurement settings. Our experiment uses multiphoton quantum simulators to mimic dynamical concurrence and three-tangle entangled systems and to track their entanglement evolutions.

Received 17 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.070502

Physics Subject Headings (PhySH)

Entanglement detection Quantum optics Quantum simulation

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Ming-Cheng Chen^1,2, Dian Wu^1,2, Zu-En Su^1,2, Xin-Dong Cai^1,2, Xi-Lin Wang^1,2, Tao Yang^1,2, Li Li^1,2,*, Nai-Le Liu^1,2, Chao-Yang Lu^1,2, and Jian-Wei Pan^1,2

¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

^*eidos@ustc.edu.cn

Measuring Entanglement in a Photonic Embedding Quantum Simulator

J. C. Loredo, M. P. Almeida, R. Di Candia, J. S. Pedernales, J. Casanova, E. Solano, and A. G. White

Phys. Rev. Lett. 116, 070503 (2016)

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Vol. 116, Iss. 7 — 19 February 2016

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Images

Figure 1
Embedding simulator for efficient entanglement measurement. The entanglement in the original dynamic system $H$ cannot be directly measured as it contains complex terms like $⟨ Ψ | A | Ψ^{*} ⟩$ . Through embedding the initial state and Hamiltonian into an enlarged simulator assisted by an ancillary qubit, the complex terms are allowed to efficiently measure on the enlarged state.
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Figure 2
The compiled embedding quantum simulators. (a) The original embedding dynamics of the concurrence system. The evolution propagator compiled from the Hamiltonian $\tilde{H}$ is encoded in the quantum circuit. Because the initial state is the product state $| 000 ⟩$ , only the first column of the propagator is involved. (b) The quantum circuit mimics the effective dynamics of the first column in the full concurrence evolution matrix, which results in a three-particle entanglement. Here, the $S$ gate is $(1, \sqrt{2}; \sqrt{2}, - 1) / \sqrt{3}$ , $H$ is the Hadamard gate, $Y$ is the Pauli $Y$ gate., and $R (t)$ is the nonunitary gate $(α, 0; 0, β)$ . (c) The photonic circuit topology to implement the concurrence effective quantum circuit. The principle of interference is detailed in the Supplemental Material [27]. (d)–(f) The original embedding dynamics, the effective quantum circuit, and the photonic circuit topology for the three-tangle dynamics, respectively. (g) The experimental setup. Ultraviolet (UV) femtosecond laser pulses (394 nm, 120 fs, 76 MHz) pass through two type-II BBO crystals to produce two pairs of entangled photons. Two single photons, one from each pair, are mixed on a PDBS to generate a $W$ -type entangled state. To simulate the three-tangle system, the PDBS is switched to a PBS to generate the GHZ-type entangled four photons. The multiphoton sources are sent to the next stage to perform local operations by HWPs and a polarization-dependent Mach-Zehnder interferometer. Finally, the photons are measured by fourfold coincidence counting. Here, BBO is beta-barium borate, PDBS is the polarization-dependent beam splitter with a transmission of 0.72 for $H$ photons and 0.28 for $V$ photons, PBS is the polarization beam splitter, HWP is a half-wave plate, QWP is a quarter-wave plate, and $H$ and $V$ denote horizontal and vertical polarization.
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Figure 3
Experimental results of entanglement dynamics in the concurrence system. (a),(b) The time-dependent expectation of observable $Z Y Y$ and $X Y Y$ . (c) The concurrence computing from two measurements of $Z Y Y$ and $X Y Y$ . The error bars represent Poissonian statistics in the photon counting. The red curves are the theoretical simulation counting for the imperfect interferometric visibility and the gray curves are the theoretical simulation without noise.
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Figure 4
Experimental results of entanglement dynamics in a three-tangle system. (a)–(f) The time-dependent expectation of observable $Z X Y Y$ , $X X Y Y$ , $Z Z Y Y$ , $X Z Y Y$ , $Z I Y Y$ , and $X I Y Y$ . (g) The three-tangle computing from the previous six measurements. The error bars represent Poissonian statistics in the photon counting. The red curves are the theoretical simulation counting for the imperfect interferometric visibility and the gray curves are the theoretical simulation without noise.
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