## Abstract

Multi-partite entangled states are important for developing studies of quantum networking and quantum computation. To date, the largest number of particles that have been successfully manipulated is 14 trapped ions. Yet in quantum information science, photons have particular advantages over other systems. In particular, they are more easily transportable qubits and are more robust against decoherence. Thus far, the largest number of photons to have been successfully manipulated in an experiment is six. Here we demonstrate, for the first time, an eight-photon Greenberger–Horne–Zeilinger state with a measured fidelity of 0.59±0.02, which proved the presence of genuine eight-partite entanglement. This is achieved by improving the photon detection efficiency to 25% with a 300-mW pump laser. With this state, we also demonstrate an eight-party quantum communication complexity scenario. This eight-photon entangled-state source may be useful in one-way quantum computation, quantum networks and other quantum information processing tasks.

## Introduction

The creation and coherent manipulation of multi-photon entangled states has a crucial
role in photonic quantum-information processing. In most cases, a pulse-pumped
spontaneous parametric down-conversion (SPDC) process is used for the generation of
multi-photon entangled states in which *n* photon pairs from the SPDC's
*n*th-order emission are available. In particular, polarization-entangled
Einstein–Podolsky–Rosen (EPR) pairs are often used as the basic
blocks for generating multi-photon entangled states or as resources for performing
quantum teleportation tasks. A number of experiments involving two photon pairs^{1,2,3,4,5,6,7,8} and a few experiments involving five photons (two
photon pairs plus one single photon)^{9} or three photon pairs^{10,11,12,13} have been carried out to demonstrate various protocols in
quantum communication and linear optical quantum computing. Typical systems for
two-photon-pair experiments use a frequency-doubled Ti:sapphire mode-locked laser as a
pump, with a repetition rate of ~80 MHz, a pulse duration of ~150
fs, and an operating wavelength of ~400 nm. The improvement in moving from
two-photon-pair to three-photon-pair experiments depends on the pump power being
increased from 600 mW to 1 W through the use of a high-power continuous-wave laser to
pump the mode-locked laser^{14}. However, the sixfold coincidence count
rates under this pump power are still low, and it is difficult to increase the pump
power further in order to manipulate more photon pairs.

In fact, other methods have been developed in recent years that are capable of generating
more photon pairs under moderate pump power, such as sources obtained using spontaneous
processes in waveguide structures^{15} or photonic crystal fibres^{16,17}. More recently, an ultraviolet enhancement cavity suitable for
multi-photon experiments was implemented by Roland Krischek *et al*.^{18} This system can provide greater than 7 W ultraviolet pump power for SPDC processes,
which also makes the generation of more photon pairs possible. However, because of the
nature of spontaneous processes, the probability *μ* of generating one
photon pair per pump pulse should normally be restricted to less than 0.1 such that the
noise from higher order photon-pair emission can be neglected. For an experiment
involving *n* photon pairs from a spontaneous process, the 2*n*-fold
coincidence counting rate can be roughly estimated as
*C*_{2n}=*fμ*^{n}*η*^{2n},
where *f* is the pump laser repetition rate and *η* is the total
detection efficiency, which is the product of all efficiencies between the source and
detector. Thus, under the limit of *μ*≤0.1, a key parameter
for a good multi-photon source is the value of *η*, which significantly
affects *C*_{2n}, especially for large *n*.

In this study, for the first time, we demonstrate an experiment involving genuine
eight-photon entanglement, which is achieved by improving *η* to 0.25 and
setting *μ* to be 0.046. With this source, we demonstrate an eight-party
quantum communication complexity scenario using an eight-photon
Greenberger–Horne–Zeilinger (GHZ) state with a fidelity of
*F*=0.59±0.02. Our experimental result has a success probability
largely exceeding the classical limit of 56.25%, which shows that the eight-photon
entangled state we prepared violates the Mermin inequality^{19}.

## Results

### Theoretical schemes

Communication complexity problems (CCPs)^{20} describe the
communication cost incurred in performing distributed computation tasks among a
number of separated parties, with each party holding his or her own input data
at the beginning. As the quantum mechanical counterpart of CCPs, quantum
communication complexity problems (QCCPs) involve the same problems, but the
different parties communicate by sending quantum bits instead of classical
bits^{21} (or by sending classical bits through previously
shared entanglements^{22}). It has been shown^{23,24}
that QCCPs can have quadratic or even exponential superiority over classical
communication complexity in some cases. It has also been proven that a violation
of Bell inequalities is the necessary and sufficient condition for QCCPs to
outperform classical CCPs^{25}.

The special quantum communication complexity scenario (QCCS) that we demonstrate
in our experiment is an eight-party version of Buhrman's model^{26}.
Suppose that there are eight parties *A*1, *A*2,...,*A*8
receiving data *X*_{1},
*X*_{2},...,*X*_{8}, respectively, where
*X*_{i}*U*{0,
1}^{2}, *i*=1, 2,...,8, and

The common objective of each party is to obtain the correct value of the Boolean function

*X*_{1},...,*X*_{8} can each be written in binary
notation as *x*1_{1}*x*1_{0},...,
*x*8_{1}*x*8_{0}. Under the conditions of equation (1), for any input
*X*_{1},...,*X*_{8}, the value distributions of
*x*1_{0},...,*x*8_{0} should be one of 128
possible combinations, which can be divided into five groups, namely,
0^{8}, 0^{6}1^{2},
0^{4}1^{4}, 0^{2}1^{6} and
1^{8}. Here 0^{i}1^{j}
stands for a combination that has *i* bits of 0 and *j* bits of 1,
regardless of the order in which they appear. The Boolean function *F* can
be rewritten as

where

That is, *F*_{0}=0 for the groups 0^{8},
0^{4}1^{4} and 1^{8}, whereas
*F*_{0}=1 for 0^{6}1^{2} and
0^{2}1^{6}.

In the classical situation, the maximum success probability for this scenario is

where *N* is the number of parties. In our case, *N*=8 so that
. Using quantum protocols, the eight
parties *X*_{1}−*X*_{8} that share a prior
eight-qubit GHZ state can have a success probability of . The protocol is shown below.

The eight-qubit GHZ state is

Each party holds a qubit of and applies rotations
*R*(*x*) or *R*(*y*) to the qubit according to the value
(that is, 0 or 1) of its own classical bit *xi*_{0},
*i*∈1, 2...8, where

Next, the party measures its qubit in the 0/1 basis and obtains the result
*yi*∈{0, 1}. After that, each party
*X*_{i} broadcasts a bit
and can derive the correct value of *F* as

with a success probability of 100%.

### Experimental realization of eight-photon GHZ state and QCCS

We now proceed with the experimental description of how to generate the
eight-photon GHZ state and demonstrate the QCCS scheme. Four specially designed
ultrabright 'beam-like' EPR sources (S1 to S4)^{27} were used in the
experiment to provide polarization-entangled EPR photon pairs. The experimental
set-up is illustrated in Figure 1. A pulsed ultraviolet
laser beam was split into two beams by a 50/50 nonpolarizing beam-splitter, and
each beam was subsequently passed through two pairs of β-barium borate
(BBO) crystals serving as the pump. Finally, 4 EPR pairs were generated in 8
different spatial modes, numbered from 1 to 8. The reason for using two pump
beams, each generating two EPR pairs, instead of using one pump beam generating
four EPR pairs, was to reduce the number of lenses that the pump beam passed
through before pumping the latter two EPR sources (S3 and S4). Passing through
too many lenses would lead to a large decrease in the down-converted photon
detection efficiency, for example, a decrease from 0.23 to 0.21. Furthermore,
all of the lenses were optimized according to their focal lengths to obtain the
highest collection efficiency *η* and a moderate production
efficiency *μ*. The focal lengths of L1, L2, L3 and L4 were 150
mm, 85 mm, 150 mm, and 85 mm, respectively, and the distances between S1 and S2
and between S3 and S4 were both 300 mm.

To achieve the best stability of the system, eight polarization-preserving
single-mode fibres were placed as close as possible to the BBO crystals to
collect the down-converted photons in the eight spatial modes. In addition, we
also constructed a new type of frequency doubler to improve the total detection
efficiency *η* (Methods), which significantly increases the
eight-photon coincidence rate without increasing the generation probability
*μ*, thus keeping the noise of higher order
photon-pair-emission from increasing. With these techniques and using only 300
mW pump power for each 'beam-like' EPR source, we observed
~22×10^{4} s^{−1}
photon pairs from each EPR source.

The photon pairs were prepared according to the Bell state , where *H* and *V* denote horizontal and
vertical polarization, respectively. The visibility with respect to the
*H*/*V* (+/−) basis under 300 mW pump power was
measured to be 96% (93%) where . The outputs of
these fibres were directed to polarization beam-splitters (PBS) to perform
post-selected fusion operations^{28} between modes 1 and 3 (PBS1),
and 6 and 7 (PBS2) or polarization-projection measurements for modes 1, 4, 5 and
8. Next, the transmitted modes of mode 3 and 7 after PBS1 and PBS2 were directed
to PBS3 for another fusion operation. An eight-photon GHZ state was prepared by
postselecting one and only one photon in each of the eight modes labelled
1′, 2′, 3′, 4′, 5′,
6′, 7′ and 8′. Next, in each mode, a quarter
wave-plate (QWP) and half-wave-plate (HWP) were used to perform the
*R*(*x*) or *R*(*y*) rotations (depending on the value
of *xi*_{0}), and a PBS was placed after the HWP to derive the
*H*/*V* basis measurement, where a result of |*H*›
denotes 0 and a result of |*V*› denotes 1. Finally, the photons
were spectrally filtered (Δ*λ*_{FWHM}=3
nm) for good temporal indistinguishability and detected by space-coupled
single-photon detectors for better collection efficiency. Note that the spatial
modes were filtered by previous single mode fibres. Two single-photon detectors
were employed for each photon, with one to detect *H* polarization and the
other to detect *V* polarization. A homemade, programmable, 16-channel
coincidence unit was used to simultaneously register all possible coincidences
among the 16 single-photon detectors.

Because of the long data collection period in our experiment (~60 h for one measurement basis) and strong focus of the ultraviolet laser beam on down-conversion BBO crystals, we also proposed an anti-burning method to avoid damage to the BBO crystals caused by the laser beam. For this method, each EPR pair source was mounted on a translation stage that moved up and down repeatedly in a small region to reduce heating due to the strongly focused ultraviolet pulses. This anti-burning system provided good stability to the pump power after it passed through the BBO crystals. Using this method, the stable time of the pump power (defined as the variation of pump power being less than ±2%) greatly increased from less than 2 h to months. It is also worth noting that in our experiment, the interference of two independent photons occurred between the outputs of two single-mode fibres mounted on stable translational stages. This adaptation greatly improved the stability of our interferometer. Under 300 mW pump power for each SPDC source, the average visibility of Hong–Ou–Mandel (HOM) interferences between independent photons overlapped on PBS1, PBS2 and PBS3 was observed to be ~73%.

We can verify genuine eight-photon entanglement of our prepared eight-photon GHZ
state using the witness^{29}

where

and

The state fidelity can then be directly calculated as

Figure 2a shows the eightfold coincidence counts of our
prepared eight-photon GHZ state measured in *H*/*V* basis.
Approximately 80 eight-photon events were observed in 64 h for the two desired
columns of *HHHHHHHH* and *VVVVVVVV*, while undesired events in the
other 254 columns clearly showed effects from the higher order photon-pair
emissions in our experiments. The effect from PBS imperfections was small,
because every PBS in our system had an extinction ratio of more than 300:1 for
both output ports. From Figure 2a, the value of observable
was calculated to be 0.75±0.03.
Figure 2b illustrates the expectation values of
*M*_{k}, *k*=1, ..., 8. Each expectation value was
derived from a complete set of eight-photon coincidence counts (256 kinds)
obtained by measuring each photon on the basis of . We obtained an averaged expectation value of
(−1)^{k}
*M*_{k} of from Figure 2b. Therefore, we can evaluate the expectation value
of *W*_{G} as
‹*W*_{G}›=−0.09±0.02,
which clearly shows the presence of genuine eight-photon entanglement.
Therefore, the fidelity of our prepared GHZ state was according to equation (11).

To demonstrate the eight-party QCCS, there were 128 kinds of possible inputs of
*X*_{1}, ..., *X*_{8}, and eight communication
parties were expected to perform different local rotations on their qubits for
different inputs. Measuring all 128 possible cases was difficult, because of the
long data-collection period of ~50 h for each case. The 128 possible
cases were thus divided into five groups denoted 0^{8},
0^{6}1^{2}, 0^{4}1^{4},
0^{2}1^{6} and 1^{8}, as mentioned
above. Therefore, in our experiment, we only studied one case in each group
(that is, 00000000, 11000000, 11110000, 11111100, and 11111111). Because of the
symmetry of our state-generation setup, it is reasonable to assume that
exchanging the places of 1 and 0 among the eight parties would yield no
differences in the experimental results. Figure 3 shows
the measured success and fail probabilities of the five cases. In each group,
the success probability *P*_{s} largely exceeded the
classical limit of 56.25%. In addition, the average success probability
*Pa* was 71.7±1.4%. In other words, the eight-photon state we
prepared cannot be described by local realistic theory.

## Discussion

The imperfections in our experiment had two main causes. One cause involved the
distinguishability between two independent photons and an imperfect EPR source,
which were characterized by the HOM interference visibility *V*_{HOM}
of independent photons and the entanglement visibility *V*_{Ent} of the
EPR source measured under low pump power. In our experiment, *V*_{HOM}
and *V*_{Ent} were ~82% and 97%, respectively. The other
important factor was the higher order photon-pair emissions due to the nature of
SPDC processes. The effect of this factor can be directly observed from the 256
measured eight-photon counts in the *H*/*V* basis.

In summary, we have presented a novel source that can provide four independent EPR
photon pairs for multi-photon experiments using only 300 mW pump power for each SPDC
source. The experimental setup of this source is rather simple, stable and easy to
manipulate. Using four EPR photon pairs and three fusion operations, we successfully
generated an eight-photon GHZ state with verified genuine eight-photon entanglement.
With this GHZ state, we demonstrated an eight-party quantum communication complexity
scenario in an experiment, with the result exceeding the classical limit of the
eight-party communication complexity scenario. A number of further applications can
be imagined with our eight-photon entanglement source; for instance, the
demonstration of various protocols in multiparty quantum networking^{12,30}, loss-tolerant one-way quantum computing using cluster
states^{31}, high-resolution quantum optical metrology with
multiphoton states^{32}, and tests of Bell's theorem without
inequalities and alignments^{33}. In recent years, the planar integrated
optics approach of optical quantum circuits has shown tremendous potential for
future optical quantum information processing, such as Shor's algorithm being
demonstrated on a chip with four single photons^{34}. The integrated
optics approach has the advantages of perfect spatial overlap and a compact and
stable set-up compared with traditional table-optics systems. Therefore, the
possible combination of our high-brightness, high-collection-efficiency SPDC source
and planar integrated optics might bring further advancement to optical quantum
information technology in the future.

## Methods

### Frequency doubler for high photon-collection efficiency

The collection efficiency of the photon pairs from the SPDC source was an
important factor in reducing the data collection time in our eight-photon
experiment. On the basis of our previous beamlike EPR source^{27},
we created a new type of frequency doubler that remarkably improved the
photon-pair collection efficiency. The experimental set-up of our frequency
doubler is shown in the inset of Figure 1. In our
frequency doubler, we used a BiB_{3}O_{6} (BIBO) crystal instead
of a LiB_{3}O_{5} (LBO) or BBO crystal, and the BIBO crystal was
cut at *θ*=149.5° and *φ*=90° to
perform a type I second-harmonic generation (SHG) process. We found that the
spectral bandwidth of the output ultraviolet beam from our frequency doubler was
narrower than other frequency doublers that use LBO or BBO crystals. In our
case, the spectral bandwidth of the 390 nm laser beam was 0.9 nm (full width of
half-maximum (FWHM)). Such a narrow bandwidth of pump significantly improves the
down-converted photon-pair collection efficiency. We also found that to achieve
the best collection efficiency of photon pairs, the value of the BIBO's
phase-matching angle *θ* should be slightly different from the
value of the highest SHG output power. Another improvement of the collection
efficiency was achieved by ensuring that the focusing in the frequency doubler
was not too strong. We chose a focal length of 125 mm for the focusing lens
before the BIBO crystal to obtain the best collection efficiency while
maintaining enough SHG output power.

With the above-mentioned techniques and other arrangements for improving photon
detection efficiency described in the main text, such as splitting the 390-nm
pump beam into two beams and choosing optimized focal lengths for pump-beam
focusing, we improved the average total detection efficiency *η*
from the original value of 0.125 to 0.250. This result increased the
eight-photon coincidence counting rate by over 200 times under the same
generation probability *μ*, thereby making the eight-photon
entanglement experiment feasible.

It is important to note that because of the narrower spectral bandwidth of the 390-nm laser beam, the visibility of HOM interference between independent photons in our system decreased. In fact, when using the low power of a 390-nm laser beam (~50 mW) to remove the emission background of the higher order photon pairs, we observed an average HOM interference visibility of ~83% and ~90% when BIBO and BBO crystals were used in the frequency doubler, respectively.

## Additional information

**How to cite this article:** Huang, Y.-F. *et al*. Experimental generation
of an eight-photon Greenberger–Horne–Zeilinger state. *Nat.
Commun.* 2:546 doi: 10.1038/ncomms1556 (2011).

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## Acknowledgements

We thank Yan-Xiao Gong for helpful discussions. This work was supported by the National Natural Science Foundation of China (Grant Nos 10874162, 11074242, 11104261 and 60921091), the National Basic Research Program of China (Grant Nos 2011CB921200 and 2011CBA00200), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant No. 200729), the Fundamental Research Funds for the Central Universities (Grant Nos WK2030020004 and WK2030020007), and the Anhui Provincial Natural Science Foundation (Grant No. 11040606Q47).

## Author information

## Affiliations

### Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026,China.

- Yun-Feng Huang
- , Bi-Heng Liu
- , Liang Peng
- , Yu-Hu Li
- , Li Li
- , Chuan-Feng Li
- & Guang-Can Guo

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### Contributions

C.F.L. and Y.F.H. designed the experiment. Y.F.H., B.H.L. and L.P. performed the experiment. Y.H.L. made the 16-channel coincidence unit. Y.F.H. and C.F.L. supervised the project. L.L. and G.C.G. contributed to the theoretical analysis, Y.F.H. analysed the data and wrote the paper.

### Competing interests

The authors declare no competing financial interests.

## Corresponding author

Correspondence to Chuan-Feng Li.

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