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arXiv:1007.2510v2 [quant-ph] 19 Jul 2010

Experimental Demonstration of a Heralded Entanglement

Source

ClaudiaWagenknecht1†, Che-MingLi1,2†, AndreasReingruber1, Xiao-HuiBao1,3, AlexanderGoebel1,

Yu-Ao Chen1,3, Qiang Zhang1, Kai Chen3⋆, and Jian-Wei Pan1,3⋆

1Physikalisches Institut, Ruprecht-Karls-Universit¨ at Heidelberg, Philosophenweg 12, 69120 Hei-

delberg, Germany

2Department of Physics and National Center for Theoretical Sciences, National Cheng Kung Uni-

versity, Tainan 701, Taiwan

3Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern

Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

†These authors contributed equally to this work.

⋆e-mail: kaichen@ustc.edu.cn; jian-wei.pan@physi.uni-heidelberg.de

The heralded generation of entangled states is a long-standing goal in quantum informa-

tion processing, since it is indispensable for a number of quantum protocols1,2. Polarization

entangled photon pairs are usually generated through spontaneous parametric down con-

version (SPDC)3whose emission, however, is probabilistic. Their applications are generally

accompanied with post-selection and destructive photon detection. Here, we report a source

of entanglement generated in an event-ready manner by conditioned detection of auxiliary

photons4. This scheme profits from the stable and robust properties of SPDC and requires

only modest experimental efforts. It is flexible and allows to significantly increase the prepa-

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ration efficiency by employing beam splitters with different transmission ratios. We have

achieved a fidelity better than 87% and a state preparation efficiency of 45% for the source.

This could offer promising applications in essential photonics-based quantum information

tasks, and particularly enables optical quantum computing by reducing dramatically the

computational overhead5,6.

Quantum entanglement is one of the key resources in quantum information and quantum

foundation. Besides its fundamental interest to reveal fascinating aspects of quantum mechanics,

they are also crucial for a variety of quantum information tasks1,2. In particular, photonic entan-

gled states are robust against decoherence, easy to manipulate and show little loss, both in fiber

and free-space transmission, and thus are exceptionally well suitable for long distance quantum

communication and linear optical quantum computing6,7. Consequently, an event-ready source for

entangled photonic states is of great importance, both from the fundamental and the practical point

of views. Entanglement sources based on the probabilistic generation process of SPDC allow for

demonstrations of a number of quantum protocols, but do not permit on-demand applications, de-

terministic quantum computing and significantly limit the efficiency of multi-photon experiments.

Alternative solutions, such as the controlled biexciton emission of a single quantum dot8–10or the

creation of heralded entanglement from atomic ensembles11, face severe experimental disadvan-

tages, such as liquid-helium temperature environment and large-volume setups.

There has been considerable progress towards the demonstration of heralded photonic Bell

pairs. The scheme by Knill, Laflamme and Milburn (KLM)12provides a theoretical breakthrough

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as proof that efficient quantum computing is possible with linear optics. Although the KLM

scheme allows the nearly non-probabilistic creation of entanglement, the method they use is still

intrinsically probabilistic. The fact that the KLM scheme uses a single photon source, perfect

photon-number-resolving detectors and moreover requires a large computational capacity makes it

barely accessible experimentally. The proposal of Browne and Rudolph5comprises a significant

advance in achieving experimental implementation by using photonic Bell pairs as the primary

resource and experimentally realistic detectors. Using their proposal, the number of optical op-

erations per logical two-qubit gate reduces to ∼ 100, in contrast to the original KLM scheme,

which would have ∼ 100,000 (refs 5,6,12). Central to such a dramatic improvement is the use of

a heralded entanglement source5,6.

Various ideas based on conditional detection of auxiliary photons or multi-photon interfer-

ence were recently proposed to overcome the probabilistic character of SPDC4,13–18. Following

this line, we demonstrate an experimental realization of a heralded entangled photon source by

adopting the proposal of´Sliwa and Banaszek4. This source provides a substantial advance over

the general methods by using linear optics12,13. In the experiment, we only use commercial thresh-

old single photon counting modules (SPCM) as detectors and passive linear optics. The source is

feasible to support on-demand applications, such as the controlled storage of photonic entangle-

ment in quantum memory19to realize the quantum repeater scheme20. Moreover, it is suitable to

serveon-chipwaveguidequantumcircuitapplicationswhichpromisenewtechnologiesinquantum

optics21.

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To demonstrate the basic principle of the heralded entangled photon source, we illustrate the

scheme of´Sliwa and Banaszek4in Fig. 1. With an input of SPDC source emitted from modes a,b,

theschemeherald an entangled photonpair in c,dmodes conditionedby triggers offour photonsin

e,f modes. As an input of the optical circuit, three-pair component of the down converted photons

entangled in polarizations is utilized. The quantum state of the three-pair photon term is given by22

|Ψ3? =

1

12(ˆ a†

xˆb†

y− ˆ a†

yˆb†

x)3|vac?,

(1)

where |vac? denotes the vacuum state, and ˆ a†andˆb†are the creation operators of photons in the

modes a and b. Horizontal and vertical polarization are represented by x and y, respectively. The

optical circuit (see the Methods section) transforms |Ψ3? into4:

|Ψ′

3? =

1

√2RT2|θ?t

??Φ+?

s+

?

1 −T4R2

2

|Γ?ts.

(2)

ThefirsttermofEq.(2)iscomposedofatensorproductoftwostates: thestate|θ?t= ˆ e†

xˆ e†

yˆf†

x′ˆf†

y′|vac?

denoting one photon in each of the four trigger modes, and the maximally entangled photon pair

in the output modes

??Φ+?

s=

1

√2(ˆ c†

xˆd†

x+ ˆ c†

yˆd†

y)|vac?.

(3)

The normalized state |Γ?tsis a superposition of all states that do not exactly have one photon in

each of the trigger mode ˆ ex, ˆ ey,ˆfx′ andˆfy′. Hence, the scheme for heralded entanglement source

is clearly based on the fact that when detecting a coincidence of four single photons in the trigger

modes (ˆ ex, ˆ ey;ˆfx′,ˆfy′), the two photons in the output modes (ˆ cx,ˆ cy) and (ˆdx,ˆdy) nondestructively

collapse to the maximally entangled state |Φ+?s.

In the experiment, we will generate the three-pair photon states (1) by a photon source (see

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the Methods section) and consequently implement the transformation of the linear optical circuit.

A schematic diagram of our experimental set-up is shown in Fig. 2, which is based on the proposal

of Ref. 4.

When taking all of experimental imperfections into account (see the Methods section), it is

crucial to evaluate the performance this source. Therefore, we have measured the state preparation

efficiency and its fidelity, where the efficiency is defined by the number of heralded photon pairs

created from the source per trigger signal. For an ideal case, one trigger signal of a fourfold single-

photon coincidence perfectly heralds one photon pair creation. In our experiment performed with

standard SPCMs, obviously, additional terms yielding triggers will thus result in a reduction of

the preparation efficiency. To overcome this obstacle, we limit their emergence by decreasing the

transmission coefficients of the beamsplitter. In this regime, the probability of transmitting more

than the minimum number of photons to the trigger becomes lower and as such, the danger of

under counting photons in the trigger detectors decreases. However, enhancing the preparation

efficiency in this way will lower the over all preparation rate.

In order to show the relation between the efficiency of state preparation and the transmission

coefficients of the partial reflecting beam splitters, we have chosen BS with three different reflec-

tion/transmission (R/T) ratios: 48.6/51.4, 57.0/43.0 and 68.5/31.5 in the experiment (Fig. 2). In

what follows we will denote them by 50/50, 60/40 and 70/30, respectively, for short. This relation

is shown in Fig. 3. The experimental efficiency can be straightforwardly represented as the follow-

ing relation by the number of triggers nt, the average detection efficiency ηsfor output states, the

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number of six-fold coincidences nsamong four trigger modes and two output modes

effexp=

ns

ntη2

s

.

(4)

For each experimental detection efficiencies ηsand R/T ratio: 0.129 (50/50), 0.133 (60/40) and

0.15 (70/30), the average coincidence counts (ns,nt) observed per 10 hours are: (37,9710),

(37,4940) and (14,1347), respectively. As can be seen from Fig. 3, the experimental results are

highly consistent with theoretical estimation (see Supplementary Information):

efftheory=

R2

(1 − ηtT/2)2,

(5)

where ηtrepresents the average detection efficiency for trigger photons. Thus, with this setup

we have significantly improved the preparation efficiency in comparison with the one provided

by the standard procedure through SPDC. One can consider single input pulses of UV laser and

output photon pairs of SPDC as trigger signals and output states, respectively. The probability of

generatingoneentangledphotonpairperUV pulsemeans thepreparationefficiency ofthestandard

procedure through SPDC22.

To quantify the entanglement of the output photons and evaluate how the prepared state

is similar to the state |Φ+?s, we have determined the state fidelity by analyzing the polarization

state of the photons in the modes (ˆ c,ˆd) in the three complementary bases: linear (H/V ), diagonal

(+/−), and circular (R/L). For an experimental state ˆ ρ, the fidelity is explicitly defined by

F= Tr(ˆ ρ??Φ+?

=

4(1 + ?ˆ σxˆ σx? − ?ˆ σyˆ σy? + ?ˆ σzˆ σz?),

ss

?Φ+??)

1

(6)

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where |Φ+?ss?Φ+| =1

4(ˆI+ˆ σxˆ σx−ˆ σyˆ σy+ˆ σzˆ σz), ˆ σz= |H??H|−|V ??V |, ˆ σx= |+??+|−|−??−| and

ˆ σy= |R??R|−|L??L|. Eq. (6) implies that we can obtain the fidelity of the prepared state ˆ ρ by con-

secutively carrying out three local measurements ˆ σxˆ σx, ˆ σyˆ σyand ˆ σzˆ σzon the photons in the output

modes (ˆ cx,ˆ cy) and (ˆdx,ˆdy) (see the Methods section). In the experiment, we only used threshold

SPCMs to perform measurements. The experimental results are shown in Fig. 4. The experimental

integration time for each local measurement, with respect to different reflection/transmission ratio

of the BS, took about: 19 h (50/50), 17 h (60/30) and 36 h (70/30). For all three splitting ratios,

we recorded more than about 50 events of desired six-photon coincidences for each local measure-

ment: ∼ 65 (50/50), ∼ 58 (60/30) and ∼ 62 (70/30). As can be seen from Table 1, the measured

values for the fidelity are sufficient to violate CHSH-type Bell’s inequality23for Werner states by

three standard deviations. Since we only used threshold SPCMs as detectors, the measured coin-

cidences are then affected by unwanted events. In our experiment, the effect of the dark count rate

in the detectors on the six-fold coincidence is rather small. (About the dark count contribution, the

main part is that one detector is triggered by dark counts, and the other five detectors are triggered

by the down conversion photons. Given a three-pair state, the probability of generating a six-fold

coincidence count within any particular coincidence window is about S ∼ η6, whereas the leading

dark count contribution is about Sd∼ η5D, where D = ndt, ndis the average dark count rate of

detector, and t denotes the coincidence window. In our experiment, we have nd ∼ 300 Hz and

t = 12×10−9sec. Then it is clear that the dark count rate in detectors contribute a very small part

of the six-fold coincidences: Sd/S = ndt/η ∼ 2×10−5. Here η = 15% is used for the estimation.)

In conclusion, we have demonstrated a heralded source for photonic entangled states, which

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is capable of circumventing the problematic issue of probabilistic nature of SPDC. Such source is

based on the well known technique of type-II SPDC, which is robust, stable and needs only modest

experimental efforts by using standard technical devices. Photon number resolving detectors are

not involved in the setup, and therefore we do not endure the restriction inherent to other schemes

for implementing heralded entanglement sources13,15. To evaluate the performance of our source,

we have measured the fidelity of the output state, and demonstrated the relation between the am-

plitude reflection coefficient of the used beam splitters and the preparation efficiency of the source.

A fidelity better than 87% and a state preparation efficiency of 45% are achieved. For future ap-

plications, the simple optical circuit of our source could be miniaturized by an integrated optics

architecture on a chip using the silica-on-silicon technique24. Using waveguides instead of bulk

optics would be beneficial to stability, performance and scalability21,25. We note that during the

preparation of the manuscript presented here, we learned of a parallel experiment by Barz et al.26.

Methods

Optical circuit. The transformation of the optical circuit consists of BS and HWP operations. The

BS operation describes the following transformation of the annihilation operators of the modes ˆ ak

andˆbk(note that we use annihilation operators to denote the corresponding modes): ˆ ak=√Rˆ ck+

√Tˆ ekandˆbk =

√Rˆdk+√Tˆfk, for k = x,y. R (T) is the amplitude reflection (transmission)

coefficient of the BS. For the modesˆfxandˆfy, the transformation of HWP at −22.5◦is defined by:

ˆfx= (ˆfx′ −ˆfy′)/√2 andˆfy= (ˆfx′ +ˆfy′)/√2. The optical circuit is able to prevent false signals

rising from two-pair emission. This is an important feature of the scheme4since the creation

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probabilitiesfor two pairs are much larger than for three pairs. Furthermore, contributionsfrom the

higherordertermsofSPDC can belimitedby controllingthecorrespondingcreation probabilities4.

It is also worth noting that for a given three-pair photon state, the probability of creating a heralded

entangled state, i.e., T4R2/2, is controllable by changing the transmission coefficients of the BS,

which can be up to ∼ 0.0114.

Photon source. The required photon pairs are generated by type-II SPDC from a pulsed laser

in a β-Barium-Borate (BBO) crystal. Here, we use a pulsed high-intensity ultraviolet (UV) laser

with a central wavelength of 390 nm, a pulse duration of 180 fs and repetition rate of 76 MHz.

For an average power of 880 mW UV light and after improvements in collection efficiency and

stability of the photon sources, we observe ∼ 80×103photon pairs per second with a visibility of

V = (91 ± 3)% measured in the diagonal (+/−) basis. (The visibility is defined by V = (Nd−

Nud)/(Nd+Nud), were Nd(Nud) denotes the number of two-fold desired (undesired) coincidence

counts. Then there exists a direct connection between visibility and fidelity of a measured state ˆ ρ:

F = Tr(ˆ ρ|Ψ−??Ψ−|) =

1

4(1 + Vx+ Vy+ Vz), where Vkfor k = x,y,z denotes the visibility of

photon pair in the diagonal, circular, and linear bases, respectively. Here |Ψ−? is the singlet Bell

state.) Then the probability of creating three photon pairs is about 5.7 × 10−5per pulse, which

is ∼ 33 times larger than that of the next leading order term. The estimation of the three-pair

creation probability per pulse is based on the experimental pair generation rate and the theoretical

n-pair creation probability22pn = (n + 1)tanh2nr/cosh4r, where r is a real-valued coupling

coefficient. From the two-fold coincidence measurement result, the experimental pair generation

rate is p′= (80 × 103)/(0.152× 76 × 106) ≈ 4.7%. We assume that p1= p′, r can directly be

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derived from p1. Thus the estimated creation probability p3and p4are obtained.

Experimental imperfections. With single photon resolving detectors and 100% detection effi-

ciency, one can see that the three-pair state can provide a maximally entangled photon pair in

the output modes deterministically with a 100% probability, if and only if the remaining photons

give rise to a fourfold coincidence among the four trigger modes. With the widely used standard

SPCM, one cannot discriminate pure single photons from multi-photons which in reality leads to

a significant problem of under counting photons. Accordingly, the trigger detectors can herald a

successful event even though more than two photons from either mode (ˆ ax,ˆ ay) or (ˆbx,ˆby) or both

have been transmitted to the trigger channels. Furthermore, experimentally we were only able to

obtain an average detection efficiency of about η = 15% resulting from limited collection and

detector efficiencies. Here the mean detection efficiency is averaged over the coupling efficiency

of eight fibre couplers and the quantum efficiency of the detectors. In addition to the imperfect de-

tections, there are two other factors that affect the performance of our source: the non-ideal quality

of the initially prepared pairs and the higher-order terms of down-converted photons. For perfectly

created pairs, destructive two-photon interference effects27–29will extinguish the contribution of

two-pair emission to the trigger signal. With an experimental visibility of (91 ± 3)% imperfectly

created states may still give rise to a contribution of two-pair events that leads to the detection of

the auxiliary triggers. In addition, four-pair emission can again contribute to both the triggers and

the output. Although the experimentally estimated creation probability for a four-pair emission is

only ∼ 1.7 × 10−6per pulse and is much smaller than the probability for a three-pair photon state

∼ 5.7 × 10−5per pulse, four-pair contribution can lead to an error of the theoretical estimation of

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the expected preparation efficiency of about 4.5%. The four-pair contribution is evaluated in the

same way as the three-pair state, where the limited detection efficiency of the trigger detectors is

considered in the calculation (see Supplementary Information). In Fig. 3, the fluctuations of our

experimental data mainly result from the intrinsic statistics of detector counts, and the stability of

optical alignment.

Experimental fidelity F. Every expectation valuefor a correlation function is obtained by making

a local measurement along a specific polarization basis and computing the probability over all the

possible events. For instance, to get the expectation value of RR correlation Tr(ˆ ρ|RR??RR|), we

perform measurementsalongthecircularbasis andthen gettheresultby thenumberofcoincidence

counts of RR over the sum of all coincidence counts of RR, RL, LR and LL. All the other

correlation settings are performed in the same way. The fidelity F can then directly be evaluated.

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Acknowledgement

This work was supported by the European Commission through the European Re-

search Council (ERC) Grant and the Specific Targeted Research Projects (STREP) project Hybrid Infor-

mation Processing (HIP), the Chinese Academy of Sciences, the National Fundamental Research Program

of China under grant no. 2006CB921900, and the National Natural Science Foundation of China. C.W.

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was additionally supported by the Schlieben- Lange Program of the ESF. The authors are grateful to Dr

Xian-Min Jin for help in improving the figures.

Author Contributions

C.W., X.-H.B., Y.-A.C., Q.Z., and J.-W.P. designed the experiment. C.W., C.-

M.L., A.R., A.G., Y.-A.C., and K.C. performed the experiment. C.W., C.-M.L., A.R., X.-H.B., K.C., and

J.-W.P. analyzed the data. C.W., C.-M.L., K.C. and J.-W.P. wrote the paper.

Competing Interests

The authors declare that they have no competing financial interests.

Correspondence

Correspondence and requests for materials should be addressed to K.C. and J.W.P.

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