Heralded quantum repeater for a quantum communication network based on quantum dots embedded in optical microcavities

Tao Li, Guo-Jian Yang, and Fu-Guo Deng

Phys. Rev. A 93, 012302 – Published 4 January 2016

Abstract

We propose a heralded quantum repeater protocol based on the general interface between the circularly polarized photon and the quantum dot embedded in a double-sided optical microcavity. Our effective time-bin encoding on photons results in the deterministic faithful entanglement distribution with one optical fiber for the transmission of each photon in our protocol, not two or more. Our efficient parity-check detector implemented with only one input-output process of a single photon as a result of cavity quantum electrodynamics makes the entanglement channel extension and entanglement purification in quantum repeater far more efficient than others, and it has the potential application in fault-tolerant quantum computation as well. Meanwhile, the deviation from a collective-noise channel leads to some phase-flip errors on the nonlocal electron spins shared by the parties and these errors can be depressed by our simplified entanglement purification process. Finally, we discuss the performance of our proposal, concluding that it is feasible with current technology.

Received 21 October 2014

DOI:https://doi.org/10.1103/PhysRevA.93.012302

Physics Subject Headings (PhySH)

Quantum communication

Optical microcavities Quantum dots

Quantum Information, Science & Technology

Authors & Affiliations

Tao Li, Guo-Jian Yang, and Fu-Guo Deng^*

Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China

^*Corresponding author: fgdeng@bnu.edu.cn

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Issue

Vol. 93, Iss. 1 — January 2016

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Images

Figure 1
The spin-dependent transitions for a negatively charged exciton $X^{-}$ . (a) A singly charged QD inside a double-sided optical microcavity. (b) The spin selection rules for optical transition of a negatively charged exciton. The symbols $↑$ and $↓$ represent the excess electron-spin projections $| + \frac{1}{2} 〉$ and $| - \frac{1}{2} 〉$ along the quantization axis $(z$ direction), respectively. The symbols $⇑$ and $⇓$ represent the spin projections of the hole $| + \frac{3}{2} 〉$ and $| - \frac{3}{2} 〉$ , respectively. $R^{↑}$ $(L^{↓})$ denotes a right-circularly (a left-circularly) polarized photon propagating along (against) the quantization axis.
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Figure 2
The coefficients $| R (ω) |, | T (ω) |, | S (ω) |, | N (ω) |$ , and $P (ω)$ vs detuning $Δ / κ$ (a) for different coupling strengths $(g = 0, 0.6 κ, 1.2 κ$ , and $2.4 κ)$ with $κ_{s} / κ = 0.1$ and (b) for different leakage rates $(κ_{s} = 0, 0.05 κ, 0.15 κ$ , and $0.2 κ)$ with $g / κ = 2.4$ . $| R (ω) |$ , solid blue line; $| T (ω) |$ , solid red line; $| S (ω) |$ , dot magenta line; $| N (ω) |$ , dashed green line; $P (ω)$ , dash-dash-dot brown line. Here $Δ = ω_{c} - ω$ . $γ / κ = 0.1$ is taken by considering the typical QD micropillar parameters.
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Figure 3
Schematic architecture of the faithful entanglement distribution procedure in our quantum repeater protocol. (a) Deterministic and faithful entanglement distribution between the nodes A and B (A, B, $...$ , C and D) with the help of time-bin encoders. (b) The decoder for each quantum node. Here, the hexagon denotes the two-photon Bell source $(N$ -photon GHZ source) and the orange rounded rectangles denoted with NODE-A and NODE-B represent the quantum nodes owned by the users Alice and Bob, respectively. $PBS_{i}$ $(i = 1, 2, ...)$ is the polarizing beam splitter that transmits the $| H 〉$ polarized photon and reflects the $| V 〉$ polarized photon, respectively. ${QWP}_{j}$ $(j = 1, 2)$ represents a quarter-wave plate which is used to accomplish the transformations $| H 〉 \leftrightarrow | R 〉$ and $| V 〉 \leftrightarrow | L 〉$ . ${CPBS}_{j}$ represents the circularly polarizing beam splitter that transmits the $| R 〉$ polarized photon and reflects the $| L 〉$ polarized photon, respectively. $PC_{i}$ is a Pockels cell.
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Figure 4
Schematic diagram of the efficient PCD on the two QDs in the same node. $H_{1}$ and $H_{2}$ are two half-wave plates and each is used to complete the Hadamard rotation on the circularly polarized photons.
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Figure 5
The performance of entanglement distribution. (a) The fidelities $F_{d}^{O}$ and $F_{d}^{E}$ conditioned on different outcomes of photon detection in the entanglement distribution vs the normalized coupling strength $g / κ$ . (b) The efficiency $η_{d}$ of entanglement distribution vs the normalized coupling strength $g / κ$ . Here $η_{d} = η_{d}^{_{O}} + η_{d}^{_{E}}, γ / κ = 0.1$ , and the resonant condition $ω_{c} = ω_{X^{-}} = ω_{0}$ is adopted.
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