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 – Published 18 February 2016

Abstract

Measuring entanglement is a demanding task that usually requires full tomography of a quantum system, involving a number of observables that grows exponentially with the number of parties. Recently, it was suggested that adding a single ancillary qubit would allow for the efficient measurement of concurrence, and indeed any entanglement monotone associated with antilinear operations. Here, we report on the experimental implementation of such a device—an embedding quantum simulator—in photonics, encoding the entangling dynamics of a bipartite system into a tripartite one. We show that bipartite concurrence can be efficiently extracted from the measurement of merely two observables, instead of 15, without full tomographic information.

Received 17 June 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.070503

Physics Subject Headings (PhySH)

Entanglement detection Quantum optics Quantum simulation

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

J. C. Loredo^1,*, M. P. Almeida¹, R. Di Candia², J. S. Pedernales², J. Casanova³, E. Solano^2,4, and A. G. White¹

¹Centre for Engineered Quantum Systems, Centre for Quantum Computer and Communication Technology, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
²Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
³Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
⁴IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain

^*juan.loredo1@gmail.com

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 (2016)

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Vol. 116, Iss. 7 — 19 February 2016

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Images

Figure 1
(a) Qubits 1 and 2 evolve via an entangling Hamiltonian $H$ during a time interval $t$ , at which point quantum state tomography (QST) is performed via the measurement of 15 observables to extract the amount of evolving concurrence. (b) An efficient alternative corresponds to adding one extra ancilla, qubit 0, and having the enlarged system—the embedding quantum simulator (EQS)—evolve via $H^{(E)}$ . Only two observables are now required to reproduce measurements of concurrence of the system under simulation.
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Figure 2
Quantum circuit for the embedding quantum simulator. (a) Four controlled-sign gates and one local rotation $R_{y} (ϕ)$ implement the evolution operator $U (t) = \exp (- i g σ_{y}^{(0)} \otimes σ_{z}^{(1)} \otimes σ_{z}^{(2)} t)$ with $ϕ = g t$ . (b) A reduced circuit employing only two controlled-sign gates reproduces the desired three-qubit dynamics for inputs with the ancillary qubit in $| 0 ⟩$ .
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Figure 3
Experimental setup. Three single photons with wavelength centered at 820 nm are injected via single-mode fibers into spatial modes 0, 1, and 2. Glan-Taylor prisms (GTs), with transmittance $t_{h} = 1$ ( $t_{v} = 0$ ) for horizontal (vertical) polarization, and half-wave plates (HWPs) are employed to initialize the state. Controlled two-qubit operations are performed based on two-photon quantum interference at partially polarizing beam splitters (PPBSs). Projective measurements are carried out with a combination of half-wave plates, quarter-wave plates (QWPs), and Glan-Taylor prisms. The photons are collected via single-mode fibers and detected by avalanche photodiodes (APDs).
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Figure 4
(a) Theoretical predictions (top) and experimentally measured (bottom) fractions involved in reconstructing $⟨ σ_{x} \otimes σ_{y} \otimes σ_{y} ⟩$ (left) and $⟨ σ_{z} \otimes σ_{y} \otimes σ_{y} ⟩$ (right), taken at $g t = π / 4$ for a 10% pump power. (b) Extracted simulated concurrence within one evolution cycle, taken at 10% (blue), 30% (green), and 100% (red) pump powers. Curves represent $C = C_{PP} | \sin (2 g t) |$ , where $C_{PP}$ is the maximum concurrence extracted for a given pump power (PP): $C_{10 %} = 0.70 \pm 0.07$ , $C_{30 %} = 0.57 \pm 0.03$ , and $C_{100 %} = 0.37 \pm 0.02$ . Errors are estimated from propagated Poissonian statistics. The low count rates of the protocol, see the Supplemental Material [15], limit the number of measured experimental settings; hence, only one data point could be reconstructed at 10% pump power.
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Figure 5
Concurrence measured via two-qubit quantum state tomography (QST) on the explicit two-photon evolution, taken at 10% (blue), 30% (green), and 100% (red) pump powers. The corresponding curves indicate $C = C_{PP} | \sin (2 g t) |$ , with $C_{PP}$ the maximum extracted concurrence for a given pump power: $C_{10 %} = 0.959 \pm 0.002$ , $C_{30 %} = 0.884 \pm 0.002$ , and $C_{100 %} = 0.694 \pm 0.006$ . Errors are estimated from Monte Carlo simulations of Poissonian counting fluctuations.
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