Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system

Chuan Wang; Yong Zhang; Ru Zhang

doi:10.1364/OE.19.025685

1. Introduction

In recent years, there has been substantial interest in quantum information processing (QIP) based on quantum entanglement. The unique properties of quantum entanglement have many applications, such as quantum cryptography [1, 2], quantum dense coding [3], quantum teleportation [4], quantum repeaters [5–7] and quantum direction communication [8, 9]. However, pure entanglement is difficult to achieve in practice because of the environment noise which will decrease the entanglement of particles and reduce the success probability of QIP. Entanglement purification is used to solve this problem by which maximally entangled states can be obtained from an ensemble in a mixed entangled state. The first entanglement purification protocol (EPP) was proposed by Bennett et al. [10] in which Werner states can be purified by using controlled not (CNOT) gates and bilateral rotations. Later, EPP was improved by Deutsch et al. for quantum privacy amplification process using similar logic operations [11]. In 1998, Briegel et al. present an novel way for long distance quantum communication using quantum repeaters based on entanglement purification and entanglement swapping [12]. Thus, EPP becomes an important element in long-distance quantum communication and had been widely investigated. Pan et al. [13] introduced an EPP model resorting to polarization beam splitters (PBSs) and single photon detectors in 2001. The experimental demonstration of EPP based on linear optics was accomplished in 2003 [14]. EPP based on the parametric down-conversion (PDC) source was presented by Simon and Pan in 2002 [15] which exploits spatial entanglement to purify the entanglement in polarization degrees of freedom. Sheng et al. also proposed an EPP based on PDC source using quantum nondemolition detectors [16]. In 2008, Xiao et al. [17] proposed an EPP with frequency and polarization hyper-entanglement. In the past decades, EPP has widely been studied and there are many related research works [18–23].

Recently, there is a novel system for QIP based on a charged quantum-dot (QD) carrying a single spin coupled to an optical microcavity [24–27]. The device exploits the photon-spin entangling gate that can be achieved in this system. Auffèves-Garnier et al. presented that the neutral QD-cavity system behaves like a beam splitter in the limit of weak incoming field [28]. Hybrid entanglement is considered to be an useful resource in realizing QIP and there are various research on hybrid quantum entanglement. In 2006, quantum repeaters based on hybrid entangled states have been experimentally realized [29]. Later, Azuma et al. proposed a realistic protocol to generate entanglement between quantum memories at neighboring nodes in hybrid quantum repeaters [30]. In 2009, Waks and Monroe present a scheme of creating hybrid entanglement between semiconductor and atomic quantum systems [31]. Brask et al. proposed a hybrid quantum repeater protocol for long-distance entanglement distribution [32]. The hybrid entangled state shows entanglement in different degrees of freedom and provides a new way of QIP. In Ref. [26], they proposed an efficient way of hybrid entanglement generation using QD and microcavity coupled system in which entanglement can be realized between photon polarization and electron spins. The QD and cavity coupled system provides a novel way of building blocks required for solid-state quantum networks, such as quantum memories, entanglement swapping and quantum teleportation [27], and various quantum logic gates [33].

Motivated by the observation of reflection spectroscopy in QD and microcavity coupled system [34] and their possible use for circuit QED system, we presented an entanglement purification protocol for photon-spin hybrid entangled state exploiting the QD and microcavity coupled system. In this scheme, ancillary photon and cavity system play the role of a parity check on the spins. In our proposed protocol, both the big-flip errors and phase-flip errors can be corrected by photon and electron interaction and the fidelity of entanglement can be increased. The proposed setup can easily be realized using current technology.

This paper is organized as follows. In Sec. 2, we introduce our parity check gate model and proposed the hybrid entanglement purification protocol. In Sec. 3, we discuss the efficiency and errors on a practical implementation. Finally, in Sec. 4, we summarize our results and discus future prospects.

2. Theoretical model of hybrid entanglement purification using QD and micro-cavity coupled system

We propose to purify the noise errors of photon and electron spin hybrid entangled state using QD and microcavity coupled system. The system is composed of a singly charged QD in micropillar microcavities. Figure 1 shows a schematic of our model. The optical properties of singly charged QDs are dominated by the optical transitions of the negatively charged exciton X that consists of two electrons bound to one hole. As illustrated by Pauli’s exclusion principle, the exciton can be created by the optical excitation of the system, e.g., when a photon passes through the cavity and interacts with the electron in the coupling cavity, the left circularly polarized photon only couples with the cavity when the electron in the spin up state |↑〉 and generate the exciton X⁻ in the state |↑↓⇑〉; the right circularly polarized photon only couples with the cavity when the electron of spin is in the spin down state |↓〉 and generate the exciton in the state |↓↑⇓〉. Here |⇑〉 and |⇓〉 represent the spin direction of the heavy hole spin state.

Fig. 1 Schematic of QD and microcavity coupled system. The diagram shows the principle of hybrid entanglement generation in quantum dot and cavity coupled system.

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The Heisenberg equations of motion describing the dynamics of the cavity field operator â and the trion X⁻ dipole operator σ₋ can be written as [25, 35]

\frac{d \hat{a}}{d t} = - [i (ω_{C} - ω) + κ + \frac{κ_{s}}{2}] \hat{a} - g σ_{-} - \sqrt{κ} {\hat{a}}_{i n} - \sqrt{κ} {\hat{a}}_{i n}^{'} + \hat{H}

\frac{d σ_{-}}{d t} = - [i (ω_{X^{-}} - ω) + \frac{γ}{2}] σ_{-} - g σ_{z} \hat{a} + \hat{G}

where g represents the coupling constant,

\frac{γ}{2}

is the excition dipole decay rate. κ_s and κ are the cavity decay rate and the leaky rate, respectively. Ĥ and Ĝ are the noise operators related to reservoirs. And we denote the frequencies of the input photon, cavity mode and the spin-dependent optical transition by ω, ω_C, ω_X⁻, respectively.

In addition to Eqs. (1) and (2), we have the following relation between the incoming and outgoing field operators [25, 35]

\begin{array}{l} {\hat{a}}_{r} = {\hat{a}}_{i n} + \sqrt{κ} \hat{a} \\ {\hat{a}}_{t} = {\hat{a}}_{i n}^{'} + \sqrt{κ} \hat{a} \end{array}

here â_in and â′_in are the input field operators from different side of the cavity, â_r and â_t are the reflected and transmitted operators, respectively.

The reflection and transmission coefficients of this microcavity system can be investigated by solving the Heisenberg equations of motion for the cavity field operator and the trion dipole operator as discussed in Ref. [25] which can be described by

\begin{array}{l} r (ω) = \frac{[i (ω_{X^{-}} - ω) + \frac{γ}{2}] [i (ω_{c} - ω) + \frac{κ_{s}}{2}] + g^{2}}{[i (ω_{X^{-}} - ω) + \frac{γ}{2}] [i (ω_{c} - ω) + κ + \frac{κ_{s}}{2}] + g^{2}} \\ t (ω) = \frac{- κ [i (ω_{X^{-}} - ω) + \frac{γ}{2}]}{[i (ω_{X^{-}} - ω) + \frac{γ}{2}] [i (ω_{c} - ω) + κ + \frac{κ_{s}}{2}] + g^{2}} . \end{array}

On condition that the resonant interaction with ω_c = ω_X⁻ = ω₀, by taking g = 0, the the reflection and transmission coefficients r and t for the uncoupled cavity system can be written as

\begin{array}{l} r_{0} (ω) = \frac{i (ω_{0} - ω) + \frac{κ_{s}}{2}}{i (ω_{0} - ω) + \frac{κ_{s}}{2} + κ} \\ t_{0} (ω) = \frac{- κ}{i (ω_{0} - ω) + \frac{κ_{s}}{2} + κ} . \end{array}

For example, the spin of QD in microcavity is in the up direction with s=1/2, if a photon in the left circular polarized state is passed through the cavity, it couples with the cavity and the exciton can be generated. Thus the reflected coefficient and transmitted coefficient are described by |r(ω)| and |t(ω)|, respectively. However, the right circular polarized photon will not couple with the cavity as the right circular polarized photon only couple the cavity with the spin of QD in the down direction (s=−1/2), the reflected coefficient and transmitted coefficient are described by |r₀(ω)| and |t₀(ω)|, respectively. So the left circular polarized photon feels a coupled cavity, the reflection coefficient in Eq. (4) is equal to unity. The right circular polarized photon feels an uncoupled cavity with the coupling constant g=0, the transmission coefficient in Eq. (5) is equal to 1. This process has been developed in the quantum information processes, such as entanglement generation [24], CNot operation and Bell state analysis [26], entanglement swapping [27] and so on.

It becomes clear from the discussion above that the dynamics of photon and electron interaction in QD and microcavity coupled system can be described by the follow equations:

\begin{array}{l} | R^{↑}, ↑ 〉 \to | L^{↓}, ↑ 〉, | L^{↑}, ↑ 〉 \to - | L^{↑}, ↑ 〉, \\ | R^{↓}, ↑ 〉 \to - | R^{↓}, ↑ 〉, | L^{↓}, ↑ 〉 \to | R^{↑}, ↑ 〉, \\ | R^{↑}, ↓ 〉 \to - | R^{↑}, ↓ 〉, | L^{↑}, ↓ 〉 \to | R^{↓}, ↓ 〉, \\ | R^{↓}, ↓ 〉 \to | L^{↑}, ↓ 〉, | L^{↓}, ↓ 〉 \to - | L^{↓}, ↓ 〉, \end{array}

here |L〉 and |R〉 represent the state of the left and right circular polarized photons, respectively. The superscript arrow in the photon state indicates the propagation direction along the z axis and the arrows represent the direction of the electrons. When a circularly polarized photon passes through the cavity and interacts with QD, the photon will either be transmitted or be reflected by the cavity according to the spin direction of the QD, e.g., a right circularly polarized photon passes through the cavity with QD in spin up state, the photon will be reflected by the cavity and the polarized state of the photon and the direction of propagation will both changed. Thus the photon polarization and electron spin may get entangled if the initial electron state is superposed. The principles of photon and electron entangler is shown in Fig. 1. The entangler works as follows: when a left circularly polarized photon |L〉 passes along the −z direction through the cavity with QD spin prepared in the spin up and down superposed state

\frac{1}{\sqrt{2}} (| ↑ 〉 + | ↓ 〉)

, the resulting state will be electron and photon hybrid entangled state:

\frac{1}{\sqrt{2}} (| ↑ 〉 + | ↓ 〉) \otimes | L 〉 \to \frac{1}{\sqrt{2}} (| ↑, R 〉 + | ↓, L 〉) .

The proposed system of hybrid entangler can be further generalized to parity check gate (PCG) based on two QDs embedded in two microcavities. One input photon passes into the cavity from the first to second one in −z direction. If the spin of the two electrons are not in the same direction, the photon will leave the cavity in the upper mode and trigger the detector which indicates that the parity of the particles is odd. Otherwise, if the two electrons are prepared in the state |↑〉|↑〉 or |↓〉|↓〉, the output photon will trigger the lower mode detector which indicates that the parity of the two particles is even.

Here we assume that the electron-spin in the cavity is prepared in the spin up and down superposed state $| ϕ_{s} 〉 = \frac{1}{\sqrt{2}} (| ↑ 〉 + | ↓ 〉)$ . The photon passes through the cavity and interacts with the electron, then the photon and spin in the cavity become entangled and the state can be described as follows:

| ϕ_{s} 〉 | ψ_{p h} 〉 \to \frac{1}{\sqrt{2}} (| ↑_{s}, R_{p} 〉 - | ↓_{s}, L_{p} 〉),

here |L〉 and |R〉 represent the left and right circularly polarized state. The generic error modes on photons can be described in three forms as follows: the bit-flip error mode, the phase-flip error mode and both the two error mode. The corresponding states with errors can be written as:

| ψ_{s, p}^{+} 〉 = \frac{1}{\sqrt{2}} ({| ↑, R 〉}_{s, p} + {| ↓, L 〉}_{s, p})

| ϕ_{s, p}^{+} 〉 = \frac{1}{\sqrt{2}} ({| ↑, L 〉}_{s, p} + {| ↓, R 〉}_{s, p})

| φ_{s, p}^{-} 〉 = \frac{1}{\sqrt{2}} ({| ↑, L 〉}_{s, p} - {| ↓, R 〉}_{s, p})

At first, we discussed the purification process on the mixed ensemble with bit-flip errors. If the initial pure state ensemble is $ρ = | ψ_{s, p}^{-} 〉〈 ψ_{s, p}^{-} |$ , the bit-flip noise will effect on the photonic qubit and transform the $| ψ_{s, p}^{-} 〉$ state to $| ϕ_{s, p}^{-} 〉$ :

ρ^{'} = F | ψ_{s, p}^{-} 〉 〈 ψ_{s, p}^{-} | + (1 - F) | ϕ_{s, p}^{-} 〉 〈 ϕ_{s, p}^{-} | .

here the coefficient (1−F) indicates the probability that the photonic qubit takes place a bit-flip operation.

Figure 2 illustrates the setup for EPP based on hybrid entangled ensemble with bit-flip errors. In the following we will give the detailed analysis about the EPP process. Alice and Bob pick up two pairs of the entangled pairs from the ensemble ρ randomly. With probability F², the two pairs are in the state $| ψ_{1, 2}^{-} 〉 | ψ_{3, 4}^{-} 〉$ , here the subscripts 1 and 3 denote the electrons in each entangled states owned by Alice and the subscripts 2 and 4 represent the photons in each state on Bob’s side. In the beginning of hybrid EPP, Alice produces the input photon in the left circularly polarized state |L〉. Then the ancillary photon passes through the two cavities and Bob performs the PCG operation on his two photons. The evolution of the composite system can be described as follows:

\begin{array}{l} \frac{1}{2} (| ↑, R 〉 - | ↓, L 〉) \otimes (| ↑, R 〉 - | ↓, L 〉) {| L 〉}_{ancilla} \\ = \frac{1}{2} (| ↑, ↑, R, R 〉 + | ↓, ↓, L, L 〉 - | ↑, ↓, R, L 〉 - | ↓, ↑, L, R 〉) {| L 〉}_{ancilla} \\ \to - \frac{1}{2} [(| ↑, ↑, R, R 〉 + | ↓, ↓, L, L 〉) | R^{↓} 〉 + (| ↑, ↓, R, L 〉 + | ↓, ↑, L, R 〉) | L^{↑} 〉] . \end{array}

If the two electron spins in the two optical microcavities are in the same state (both in the states |↑〉₁|↑〉₂ or |↓〉₁|↓〉₂), the mode information of the input photon will not changed and trigger the detector in the lower mode (D2). The evolution of the composite system can be written as:

\begin{array}{l} | L^{↓} 〉 {| ↑ 〉}_{1} {| ↑ 〉}_{2} \Rightarrow - | R^{↓} 〉 {| ↑ 〉}_{1} {| ↑ 〉}_{2}, \\ | L^{↓} 〉 {| ↓ 〉}_{1} {| ↓ 〉}_{2} \to - | R^{↓} 〉 {| ↓ 〉}_{1} {| ↓ 〉}_{2} . \end{array}

Otherwise, if the two electron spins are not in the same state, the mode of the photon will be changed and detected by the detector in the upper mode (D1):

\begin{array}{l} | L^{↓} 〉 {| ↑ 〉}_{1} {| ↓ 〉}_{2} \Rightarrow | L^{↑} 〉 {| ↑ 〉}_{1} {| ↓ 〉}_{2}, \\ | L^{↓} 〉 {| ↓ 〉}_{1} {| ↑ 〉}_{2} \Rightarrow | L^{↑} 〉 {| ↓ 〉}_{1} {| ↑ 〉}_{2} . \end{array}

By detecting the output mode of the ancillary photon, one can distinguish the spin states of electron systems in the even number parity {|↑〉₁|↑〉₂, |↓〉₁|↓〉₂} or in the odd number parity {|↑〉₁|↓〉₂, |↓〉₁|↑〉₂}. If the photon reveals the detector D2, the state will collapse to

\frac{1}{\sqrt{2}} (| ↑, ↑, R, R 〉 + | ↓, ↓, L, L 〉)

. Then Alice measures the electron spin 2 in the basis

| \pm X 〉 = \frac{1}{\sqrt{2}} (| ↑ 〉 + | ↓ 〉)

. If Bob’s detection records one photon event in D3 and Alice’s measurement is |+ X〉, the remaining state is

| ψ_{1, 2}^{+} 〉

. Otherwise, they get the state

| ψ_{1, 2}^{-} 〉

.

Fig. 2 Schematic diagram showing the principle of hybrid EPP process. The input ancillary photon is in the opposite direction of the spin direction as defined. CPBS denotes the polarization beamsplitter in left and right circularly polarized mode. D1 and D2 represent single photon detectors. D3 represents the photon number resolving detection.

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Exploiting the setup shown in Fig. 2, if the initial two hybrid entangled pairs are in the state |ϕ⁻〉_1,2|ϕ⁻〉_3,4 with probability (1 − F)², the setup will evolve the composite system as

\begin{array}{l} \frac{1}{2} (| ↑, L 〉 - | ↓, R 〉) (| ↑, L 〉 - | ↓, R 〉) {| L 〉}_{ancilla} \\ = \frac{1}{2} (| ↑, ↑, L, L 〉 + | ↓, ↓, R, R 〉 - | ↑, ↓, L, R 〉 - | ↓, ↑, R, L 〉) {| L 〉}_{ancilla} \\ \to - \frac{1}{2} [(| ↑, ↑, L, L 〉 + | ↓, ↓, R, R 〉) | R^{↓} 〉 + (| ↑, ↓, L, R 〉 + | ↓, ↑, R, L 〉) | L^{↑} 〉] . \end{array}

Bob’s parity check will reveal the detector D3 with one photon event and Alice’s ancillary photon will be detected in the |R^↓〉. Under this condition, the state can not be distinguished by Alice and Bob with the case of |ψ⁻〉_1,2|ψ⁻〉_3,4 and the two pairs are preserved.

Similarly, the evolution of the other two terms |ϕ⁻〉_1,2|ψ⁻〉_3,4 and |ψ⁻〉_1,2|ϕ⁻〉_3,4 are described as

\begin{array}{l} \frac{1}{2} (| ↑, L 〉 - | ↓, R 〉) (| ↑, R 〉 - | ↓, L 〉) {| L 〉}_{ancilla} \\ = \frac{1}{2} (| ↑, ↑, L, R 〉 + | ↓, ↓, R, L 〉 - | ↑, ↓, L, L 〉 - | ↓, ↑, R, R 〉) {| L 〉}_{ancilla} \\ \to - \frac{1}{2} [(| ↑, ↑, L, R 〉 + | ↓, ↓, R, L 〉) | R^{↓} 〉 + (| ↑, ↓, L, L 〉 + | ↓, ↑, R, R 〉) | L^{↑} 〉] \end{array}

and

\begin{array}{l} \frac{1}{2} (| ↑, R 〉 - | ↓, L 〉) (| ↑, L 〉 - | ↓, R 〉) {| L 〉}_{ancilla} \\ = \frac{1}{2} (| ↑, ↑, R, L 〉 + | ↓, ↓, L, R 〉 - | ↑, ↓, R, R 〉 - | ↓, ↑, L, L 〉) {| L 〉}_{ancilla} \\ \to - \frac{1}{2} [(| ↑, ↑, R, L 〉 + | ↓, ↓, L, R 〉) | R^{↓} 〉 + (| ↑, ↓, R, R 〉 + | ↓, ↑, L, L 〉) | L^{↑} 〉] . \end{array}

These two cases are appeared with probability F(1–F) and can be distinguished by the case that Alice’s ancillary photon is detected in the lower spatial mode and Bob’s parity check reveals two photon event or none photon event on his detector D3. These two cases are discarded after EPP and we can get a new ensemble ρ′ with the fidelity of

F^{'} = \frac{F^{2}}{F^{2} + {(1 - F)}^{2}}

which is larger than F when F > 1/2.

For the hybrid entangled state with phase-flip errors, one can introduce Hadamard operations on electron spin and photon polarization to change them into bit-flip errors. The evolution of the state of |ψ⁻〉 and |ψ⁺〉 under Hadamard operations can be described as follows:

\frac{1}{\sqrt{2}} (| ↑, R 〉 - | ↓, L 〉) \overset{H_{e} \otimes H_{p}}{\to} - \frac{1}{\sqrt{2}} (| ↑, R 〉 - | ↓, L 〉),

and

\frac{1}{\sqrt{2}} (| ↑, R 〉 + | ↓, L 〉) \overset{H_{e} \otimes H_{p}}{\to} \frac{1}{\sqrt{2}} (| ↑, L 〉 - | ↓, R 〉)

It is obvious that the state with phase flip errors |ψ⁺〉 can be changed into the state |ϕ⁻〉 by simply Hadamard operations acting on the two particles. Then the two users can perform the EPP on the bit-flip errors to purify the ensemble efficiently.

3. Efficiency and experiment feasibilities

The realization of hybrid EPP relies on the electrons and photons parity check processes. For the parity check on photons, it is necessary to use photon number resolving detectors. The current experiment process has realized photon number detection with a high probability [36]. The parity check on electron spins rely on the properties of QD and microcavity coupled system. Detectors with quantum efficiencies η can be modeled by placing the transmission coefficients η in front of ideal detectors. The performance of the QD and microcavity coupled system relative to the frequency detuning and the normalized coupling strength, we employed the coupling constant g to calculate the fidelity in the coupled system to test the performance of our proposed protocol.

Figure 3 illustrates the entanglement fidelities versus coupling strength in our proposed EPP. The purification fidelity relies on the coupling strength of the QD and microcavity. Line A, line B and line C represent the fidelity after EPP with the coupling constant of the QD with micro-cavity g_A/κ = 1.2, g_B/κ = 0.3 and g_C/κ = 0.1, respectively. As show in this figure, weak coupling rapidly decrease the EPP fidelity lines. It is obvious that if the coupling strength is large than 1, the results of EPP in realistic systems is similarly with ideal conditions. If the cavity side leakage κ_s is taken into account, the entanglement fidelity after EPP with respect to the initial fidelity is described by the dotted line in Fig. 4. And the solid line represents the EPP fidelity with no leaky. The dotted line is the fidelity with cavity leaky rate κ_s = 0.05. As shown in this figure, the cavity leakage which generally decrease the entanglement fidelity in EPP.

Fig. 3 Schematic diagram showing the efficiency of hybrid EPP process. The solid line (line A) represents the EPP fidelity with g/κ=1.2. Line B and line C are for fidelity lines with coupling strength g/κ=0.3 and g/κ=0.1.

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Fig. 4 Schematic diagram showing the efficiency of hybrid EPP process in leaky cavity. The solid line represents the EPP fidelity with no leaky. The dotted line is the fidelity with cavity leaky rate κ_s = 0.05.

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State-of-the-art technology allows the realization of high quality QDs and optical microcavities. QD is considered to be an artificial atom in which Rabi oscillations have been observed between the first two energy levels of a QD [37,38]. Recently, some progresses have been made on optical spin manipulation in QDs [39–41] which provide us an useful method in controlling the spin state and measurement.

The core techniques for realizing our EPP process in the system are the long coherence time of QDs and the strong coupling of the quantum-dot with the cavity. Recent experiments have shown that the coherence time of the GaAs or InAs based QDs is longer enough [42]. The near-unity reflectance and transmittance are due to the formation of the mixed exciton cavity modes of the system. In current experiments, the strongly coupled QD and microcavity system has been demonstrated recently in various microcavities and nanocavities [43–46]. Ref. [43] reported that the coupling strength approaches to g = 0.5 in microcavity with diameter d = 1.5μm with the cavity leakage acceptable. The quality factors for the micropillars of the same size were increased to 4 × 10⁴ for diameters below d = 2μm, corresponding to g/(κ + κ_s) ≈ 2.4 by improving the sample designs and fabrication [47]. The fidelity of the proposed EPP may decrease by a factor $[1 + \exp (- \frac{t}{T^{e}})] / 2$ due to the spin decoherence, here T^e is the spin coherence time and t is the cavity photon lifetime. The spin coherence time could be extended to μs using spin echo techniques [48, 49]. This implies the feasibility of our hybrid EPP using QD in microcavity system. Therefore the proposed schemes could be implemented with current technology.

4. Summary

In summary, we have theoretically studied QND measurement of spin parity with QD and cavity coupled system and proposed a hybrid entanglement purification protocol. The parity QND requires one ancillary photon and single photon detection. Thus the parity of entangled state can be transformed to the spatial mode of the ancillary photon and the CNOT operations are not needed. Based on electron spin PCG and linear optical devices, hybrid EPP can be realized in which the two nonlocal parties can purify the initial state with a high probability.

Based on the current experimental parameters, the present scheme exhibit a high feasibility to detect the spin parity without destroying them. Therefore the interaction of QD and cavity coupled system shows a great potential as a new platform for solid quantum optics and quantum information processing.

Acknowledgments

This work is supported by the National Fundamental Research Program Grant No. 2010CB923202, Specialized Research Fund for the Doctoral Program of Education Ministry of China No. 20090005120008, the Fundamental Research Funds for the Central Universities No. BUPT2009RC0710, China National Natural Science Foundation Grant Nos. 10947151, 60937003.

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Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system

Abstract

1. Introduction

2. Theoretical model of hybrid entanglement purification using QD and micro-cavity coupled system

3. Efficiency and experiment feasibilities

4. Summary

Acknowledgments

References and links

Cited By

Figures (4)

Equations (21)

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